Was there much resistance by Roman citizens to keep worshipping Roman deities in the post-Constantine Rome?

Of particular interest to you might be the pagan revival under Julian. Before him, Constantius tried to balance the pagan and Christian scene, but Julian was a far more eccentric figure. His "conversion" away from Christianity can be seen in the following:

"The legions arrived, and I, as was customary, went to meet them and exhorted them to continue their march. For one day they halted, and till that time I knew nothing whatever of what they had determined; I call to witness Zeus, Helios, Ares, Athene, and all the other gods that no such suspicion even entered my mind until that very evening. It was already late, when about sunset the news was brought to me, and suddenly the palace was surrounded and they all began to shout aloud, while I was still considering what I ought to do and feeling by no means confident.

My wife was still alive and it happened, that in order to rest alone, I had gone to the upper room near hers. Then from there through an opening in the wall I prayed to Zeus. And when the shouting grew still louder and all was in a tumult in the palace I entreated the god to give me a sign; and thereupon he showed me a sign and bade me yield and not oppose myself to the will of the army. Nevertheless even after these tokens had been vouchsafed to me I did not yield without reluctance, but resisted as long as I could, and would not accept either the salutation or the diadem. But since I could not singlehanded control so many, and moreover the gods, who willed that this should happen, spurred on the soldiers and gradually softened my resolution, somewhere about the third hour some soldier or other gave me the collar and I put it on my head and returned to the palace, as the gods know groaning in my heart. And yet surely it was my duty to feel confidence and to trust in the god after he had shown me the sign; but I was terribly ashamed and ready to sink into the earth at the thought of not seeming to obey Constantius faithfully to the last" (Julian, Ep ad Ath. 283-284).

And Ammianus Marcellinus even says that Julian had a vision of the Roman genius:

"But the very night before the day on which he was thus proclaimed emperor, Julian had mentioned to his most intimate friends that during his slumbers some one had appeared to him in a dream, in the form and habit of the genius of the empire, who uttered these words in a tone of reproach: "For some time, Julian, have I been secretly watching the door of thy palace, wishing to increase thy dignity, and I have often retired as one rejected; but if I am not now admitted, when the opinion of the many is unanimous, I shall retire discouraged and sorrowful. But lay this up in the depth of thy heart, that I will dwell with thee no longer" (Amm. 20.5.10).

Maximus of Ephesus was one of Julian's teachers and held a good amount of sway in his life. He was involved with the Cult of Cybele and Mithraism, and was also a follower of Neoplatonism, a mystical philosophical development of Late Antiquity by the Philosopher, Plotinus (AD 205-269), passed down through Plotinus' disciple, Porphyry (AD 234-305), and his disciple, Iamblichus (AD 245-325), who incorporated eastern religious aspects into Neoplatonism.

One of Julian's works was entitled, "Against the Galilaeans" (Contra Galileos or Κατὰ Γαλιλαίων) written in the spring of AD 363. In it he heavily critiques the Christian faith, claiming that Christians are merely an off-shoot of Judaism, and a worse one at that:

"But what great gift of this sort do the Hebrews boast of as bestowed on them by God, the Hebrews who have persuaded you to desert to them? If you had at any rate paid heed to their teachings, you would not have fared altogether ill, and though worse than you did before, when you were with us, still your condition would have been bearable and supportable. For you would be worshipping one god instead of many, not a man, or rather many wretched men. And though you would be following a law that is harsh and stern and contains much that is savage and barbarous, instead of our mild and humane laws, and would in other respects be inferior to us, yet you would be more holy and purer than now in your forms of worship.

But now it has come to pass that like leeches you have sucked the worst blood from that source and left the purer. Yet Jesus, who won over the least worthy of you, has been known by name for but little more than three hundred years: and during his lifetime he accomplished nothing worth hearing of, unless anyone thinks that to heal crooked and blind men and to exorcise those who were possessed by evil demons in the villages of Bethsaida and Bethany can be classed as a mighty achievement. As for purity of life you do not know whether he so much as mentioned it; but you emulate the rages and the bitterness of the Jews, overturning temples and altars, and you slaughtered not only those of us who remained true to the teachings of their fathers, but also men who were as much astray as yourselves, heretics, because they did not wail over the corpse in the same fashion as yourselves.

But these are rather your own doings; for nowhere did either Jesus or Paul hand down to you such commands. The reason for this is that they never even hoped that you would one day attain to such power as you have; for they were content if they could delude maidservants and slaves, and through them the women, and men like Cornelius, and Sergius. But if you can show me that one of these men is mentioned by the well-known writers of that time,----these events happened in the reign of Tiberius or Claudius,----then you may consider that I speak falsely about all matters" (Jul. Cont. Gal, 201E).

as well as the following:

And why is it that you do not abide even by the traditions of the Hebrews or accept the law which God has given to them? Nay, you have forsaken their teaching even more than ours, abandoning the religion of your forefathers and giving yourselves over to the predictions of the prophets? For if any man should wish to examine into the truth concerning you, he will find that your impiety is compounded of the rashness of the Jews and the indifference and vulgarity of the Gentiles. For from both sides you have drawn what is by no means their best but their inferior teaching, and so have made for yourselves a border of wickedness.

For the Hebrews have precise laws concerning religious worship, and countless sacred things and observances which demand the priestly life and profession. But though their lawgiver forbade them to serve all the gods save only that one, whose "portion is Jacob, and Israel an allotment of his inheritance"; though he did not say this only, but methinks added also "Thou shalt not revile the gods"; yet the shamelessness and audacity of later generations, desiring to root out all reverence from the mass of the people, has thought that blasphemy accompanies the neglect of worship.

This, in fact, is the only thing that you have drawn from this source; for in all other respects you and the Jews have nothing in common. Nay, it is from the new-fangled teaching of the Hebrews that you have seized upon this blasphemy of the gods who are honoured among us; but the reverence for every higher nature, characteristic of our religious worship, combined with the love of the traditions of our forefathers, you have cast off, and have acquired only the habit of eating all things, "even as the green herb." But to tell the truth, you have taken pride in outdoing our vulgarity, (this, I think, is a thing that happens to all nations, and very naturally) and you thought that you must adapt your ways to the lives of the baser sort, shopkeepers, tax-gatherers, dancers and libertines" (Jul. Cont. Gal, 238A).

Moreover, Julian tried to revive the old pagan practices with things like organising the pagan cults into a more cohesive set (Julian, Ep. 22) and having large scale sacrifices:

He offered repeated victims on the altars of the gods; sometimes sacrificing one hundred bulls, and countless flocks of animals of all kinds, and white birds, which he sought for everywhere by land and sea; so that every day individual soldiers who had stuffed themselves like boors with too much meat, or who were senseless from the eagerness with which they had drunk, were placed on the shoulders of passers-by, and carried to their homes through the streets from the public temples where they had indulged in feasts which deserved punishment rather than indulgence. Especially the Petulantes and the Celtic legion, whose audacity at this time had increased to a marvelous degree.

And rites and ceremonies were marvelously multiplied with a vastness of expense hitherto unprecedented; and, as it was now allowed without hindrance, every one professed himself skillful in divination, and all, whether illiterate or learned, without any limit or any prescribed order, were permitted to consult the oracles, and to inspect the entrails of victims; and omens from the voice of birds, and every kind of sign of the future, was sought for with an ostentatious variety of proceeding" (Amm. Marc. 22.12.6-7)

Still, one of my favourite things he did was bring back all the Christian bishops from exile, "I have remitted their sentence of exile for all in common who were banished in whatever fashion by Constantius of blessed memory, on account of the folly of the Galilaeans. But in your case, I not only remit your exile, but also, since I am mindful of our old acquaintance and intercourse, I invite you to come to me. You will use a public conveyance as far as my headquarters, and one extra horse" (Julian, Ep. 15 -- To Aetius). What better way to get the Christians to quarrel and fracture internally than to bring back all their squabbling members from exile? (I'm sorry, but I always find that part hilarious).