The easy and simple answer to this question is yes. Christian abolitionists, such as William Wilberforce, John Wesley (founder of Methodism) and others, had had great success in mustering religious communities to fight slavery and did indeed engage in theological debate on whether the Bible endorsed slavery.
Below is a selection from Wilberforce's A Letter on the Abolition of the Slave Trade which explicitly addresses why, in Wilberforce's opinion, many verses cannot be held to endorse slavery in the age of Christianity.
It is however, most of all astonishing, that our opponents attempt to vindicate the slave trade on grounds of religion also. The only argument which they urge with, the slightest color of reason is that slavery was allowed under the Jewish dispensation. The Jews were exalted by the express designation of heaven to a state of eminence above the strangers who sojourned among them, and the heathen who dwelt around them, from either of whom, as a mark of their own dominion, God, who has a right to assign to all his creatures their several places in the scale of being, allowed them to take bondmen and bondwomen, treating them, however, with kindness, remembering their own feelings when they were slaves in Egypt, and admitting them to the chief national privileges, to the circumcision, to the passover, and other solemn feasts, and thus instructing them in the true religion. Besides this, the slaves were to be set free at the year of Jubilee, or every fiftieth year, a command which was alone sufficient to prevent their accumulating in any great number.
But they who thus urge on us the Divine toleration of slavery under the Jewish Theocracy, should remember that the Jews themselves were expressly commanded not to retain any of their own nation, any of their brethren in slavery, except as a punishment, or by their own consent; and even these were to be set free on the return of the sabbatical, or the seventh year. Inasmuch therefore, as we are repeatedly and expressly told that Christ has done away all distinctions of nations, and made all mankind one great family, all our fellow creatures are now our brethren; and therefore the very principles and spirit of the Jewish law itself would forbid our keeping the Africans, any more than our own fellow subjects, in a state of slavery
His primary claim is that God forbade any permanent slavery of fellow members of the Jewish people. Combining this with his claim that "Christ has done away all distinctions of nations," no man can be enslaved by a Christian without violating his religion.
This is simply one argument about whether the Bible can condone slavery and there were many others. Admittedly, this example is from Britain, not the United States, but if you wanted something more concretely American to refute the southern slaveholder, I would point you to the foundation of the Southern Baptist Convention, which was formed by way of a schism over the issue of slavery when the mission board for the Baptists refused to commission any missionaries that owned slaves. This split shows that there was a fierce divide over the issue of Christian slave-holding rather than a simple acceptance.
But even after that split, it did not become a simple divide between north and south. Numerous theological texts were written arguing that slavery cannot be supported by the Bible. One example is A Condensed Anti-Slavery Bible Argument; By a Citizen of Virginia written by George Bourne. His approach is far more "academic" in that it attempts to argue that even old testament verses cannot be used to defend slavery and that the practice never really existed under the Hebrews.
Preparatory to a critical examination of the celebrated statute contained in Lev. xxv. 44-46, it will be necessary to correct the common English translation of it, the same being the falsest translation I ever saw. The exact literal translation of it is as follows: verse 44--"And thy man servant, and thy maiden, which shall be to thee (shall be) from the nations which surround you. From them shall ye procure (the) man servant and the maiden."
Verse 45. "And also from the sons of the foreigners, the strangers among you, from them shall ye procure--and from their families which (are) among you, which they brought forth into your land, and (they) shall be to you for a possession."
Verse 46. "And ye shall possess them yourselves for your sons after you, for to possess (as) a possession. For ever of them shall ye serve yourselves. And over your brethren the sons of Israel, man towards his brother, thou shalt not rule over with rigor."
This is as exact a literal translation of the statute as can be made, though the phraseology of it may be so varied in several instances, as to read in a more elegant English idiom, without any alteration or variation of its true meaning. The words wanting in the Hebrew text, but supplied for the sake of perspicuity and precision in English, are enclosed in brackets. The slightest comparison of this with the common English translation, will show how false and absurd the latter must be. Thus the two Hebrew words evedh and amau, falsely translated "bond men" and "bond maids" in the common translation, are both in the singular number in the Hebrew text, literally meaning "manservant" and "maid" or "maiden," in Hebrew, and as such are correctly translated "servant" and "maid" in the common translation of the 6th verse of the same chapter!! The word "quaunah," improperly translated "buy" in the 44th and 45th verses, ought to have been literally rendered, procure, acquire, obtain, &c., in the same passages. The Hebrew word goim, falsely translated "heathen" in the 44th verse, always literally means "nations," and should in whatever it occurs be thus rendered. The Hebrew word nauhal, rendered "possess" in my translation, which is the nearest to its literal meaning, may sometimes perhaps be correctly rendered "inherit," "redeem," &c., according to the subject matter treated of, as it is in some parts of the English Scriptures, but which do not express its true meaning in the present case, as we shall soon see. The true meaning of these words was thus perverted in the common translation, because since there were no words in the Hebrew language answering to our English word "slave," "slaveholder," "slavery," &c., King James' translators, in imitation of the Catholic priests who first forged these perversions, falsely dressed up their English version of this statute, so as to resemble the modern Christian practice of negro slavery as nearly as possible--that species of slavery having at the period of their translation, under the sanction of these and similar perversions of the Scriptures, become very extensive, respectable, and popular, in several Christian countries, especially in their tropical territories. Like the false priests and Pharisees of old, these translators, in connection with many other corruptionists of their time, and with still more now existing, thus falsified the true word of God to gratify a corrupt public sentiment, and please their principal patrons for the sake of worldly popularity.
This statute was rendered necessary in the Levitical code from the fact, that by the operation of the statutes for the original distribution of land and the institution of the Jubilee, it was impossible for foreigners settling in the Israelitish nation and for their posterity to hold any real estate except during very short periods, so that it was necessary for them and their posterity, so long as they remained in the nation, to be the servants of the native Israelites, the lineal descendants of Abraham and Shem. It was in this sense alone that the Jewish nation as such, and not the individuals composing it, were to "inherit," or rather possess these adopted foreigners and their posterity, for the purpose of free and voluntary service only.
I highlight this particular argument to illustrate the extent of this type of argument. Bourne focuses his criticism of classic Old Testament defenses of slavery on two fronts: translation errors and consideration of Hebrew laws forbidding foreign land ownership. In the passage quoted above, he claims that the translators of the King James Bible, the primary English translation of the day, read their slaver biases into the text and that the words they translate as "slave" actually mean servant. He combines this idea with the fact that all land in Israel must be owned by Israelites or revert to Israelite ownership every seven years by law. Bourne argues that the only way for any foreigner to have any security in their home and living situation was to technically be a servant of a landholding Israelite. Therefore, these servants are not slaves, but second class citizens employed by Israelites but still retaining rights as free men and women. I will not speak to the strength of such an argument, but I think that Wilberforce and Bourne provide a decent view of the types of arguments being made: either to allow that Jews owned slaves but Christ forbid Christians from doing the same or to attempt to prove that Jews could not own slaves themselves and slavery was not part of the Judeo-Christian world.
There were many other Christian abolitionist movements in the United States as well. The Quakers and Methodists have a long history of abolitionism, as do many Baptist groups. However, I do not want to give the impression that being a Christian who defended slavery was a fringe or minority position. Opposition to Abolitionism was fierce in both secular and religious circles.
I'd like to add that the mainstream voice of Christianity in America was often either silent or pro-slavery; and that the Christians who were most often strongly abolitionists most often belonged to denominations that were proud of being a little different than your standard issue Episcopalian or Lutheran. As in secular society, churches split over slavery: the Methodist church was the largest denomination in mid-nineteenth century America, and it divided as a direct result of the the slavery question.
When I teach the relationship between American Christianity and slavery, I like to use Frederick Douglass as an example of how a anti-slavery radical related to Christianity. While still enslaved, he taught a secret Sunday School for other enslaved people. After he escaped slavery, he moved to Massachusetts and was shocked and disappointed by the condescension and indifference to slavery he found in the Methodist church. He became an ordained minister in the AME church but left after a few years, saying that it was complicit in holding other African-Americans in slavery.
When he published his Narrative, he wrote about the conflict he found in American Christianity:
"I love the pure, peaceable, and impartial Christianity of Christ: I therefore hate the corrupt, slaveholding, women-whipping, cradle-plundering, partial and hypocritical Christianity of this land. Indeed, I can see no reason, but the most deceitful one, for calling the religion of this land Christianity. I look upon it as the climax of all misnomers, the boldest of all frauds, and the grossest of all libels."
Most of my students are surprised at the degree to which Douglass excoriates the American church in his Fourth of July speech; I think they're expecting something like King's I Have a Dream speech, filled with religious iconography but focused on uplifting oppressed people. But Douglass returns again and again to the hypocrisy of slavery in a land where the Bible and the Constitution are venerated, and you can make a strong argument that a full third of the speech takes on the religious side of this.
So the answer to your question is yes, many American Christians argued against slavery. Most people who argued against slavery were Christians, and a very large proportion of those people would say that they argued against slavery because they were Christians. But most broad American institutions, including the American church, tended to either explicitly or implicitly support slavery, much to the anger and frustration of Christian anti-slavery activists.
Yes: George Bourne among others:
5 And if thy brother, a Hebrew man, or a Hebrew woman, be sold unto thee, and serve thee six years; then in the seventh year thou shalt let him go free from thee--Deut. xv. 12.
By force of this one short Levitical statute, the act of man-stealing (kidnapping), man-selling (slave-trading), and man-holding (slaveholding), are, like several other crimes, condemned by the Levitical law; declared by the statute to be punishable with sure death--it being very remarkable that the sentence of punishment is expressed in the strongest terms, see 1Lev. xxiv. 17,
Bourne also used the example of Joseph, sold by his brothers into slavery:
The crime committed upon him was, therefore, stealing, and as he was a man that crime was "manstealing," the nature and consequences of which were precisely the same as those which everywhere uniformly attend the practice of human slavery, or in other words, they are each precisely the same crime. It should be remarked in further illustration, that the barbarities and horrors which uniformly attend the practice of human slavery, as incidents to it, absolutely necessary to its support, are not recorded in this case as a part of the great crime so severely condemned. Notwithstanding his "anguish of soul," Gen. xlii. 21, we do not know but Joseph was as "well treated" as the best conditioned of our slaves now are. The whole moral guilt of the transaction is represented in the passage quoted, as consisting in the conversion of Joseph into an article of property, or rendering him a slave. This case is also highly instructive by its teaching us that human slavery is as great a crime against the law of nature, as it is against the Scriptures or law of Revelation. The latter not having been revealed to the Patriarchs, they were left to the guidance furnished by the dim light of the former, in consequence of which they committed many crimes, against both of these laws, of which they did not become sensible till they were brought into deep trouble by the same.
By similar means the strongest advocates of human slavery may be convinced of its deep natural as well as revealed criminality, and it is indeed often the last argument that can be effectually used with such persons. Let them and their relations and friends be but once enslaved themselves, and they will as readily see and acknowledge the natural and moral guilt of the practice, as Joseph's brethren did.
It was the Old Testament that slaveowners would cite to justify their use of slaves. In citing passages from it, Bourne was in a way carrying the war into the enemy camp, showing how the slavery of the Bible and the slavery of the South differed: these were a people stolen and sold, and the thieves guilty of a crime.
But the essential Abolitionist argument was not from the Old but the New Testament: the central principle that all people are equal before God. This was an uncomfortable argument for many: it was a racist time, and many Whites, even those opposed to slavery, would have thought African Americans to be unequal to Whites. That discomfort allowed the slaveholders to advance the idea that slavery was paternalistic, that slaveholders were taking care of their inferior slaves. That this form of slavery- perpetual, racially-based slavery- did not have an Scriptural basis was of course ignored.
Bourne, George ( 1845)A CONDENSED ANTI-SLAVERY BIBLE ARGUMENT; BY A CITIZEN OF VIRGINIA. S.W. Benedict