Everything I've ever heard regarding the US motives to go to war with Mexico was focused around slavery. What other reasoning existed for the politicians of the day, as well as the citizens?
U. S. Grant later wrote, "one of the most unjust [wars] ever waged by a stronger against a weaker nation. It was an instance of a republic following the bad example of European monarchies, in not considering justice in their desire to acquire additional territory." Likewise, Alexander Stephens (the author of the later Cornerstone of the Confederacy speech did not have overly strong objections to slavery) said, "The principle of waging war against a neighboring people to compel them to sell their country is not only dishonorable, but disgraceful and infamous."
On February 9, 1847, John Calhoun (rather unhostile to slavery, and you might call him a Democrat) gave a speech decrying the war. He mentioned "a very large portion of the people honestly believe that the war might and ought to have been avoided; that it was commenced by the Executive without the sanction of Congress or the Consititution, and that it is hightly inexpedient and injurious". He mentioned the morality of helping a fellow federal republic, that it was pointless to war further in central Mexico to try (perhaps vainly) to compel acceptance of that which the US could simply seize (to wit, more northerly territory), occupation either temporary or permanent would be long, expensive, and dangerous (guerilla war, citing Florida). And he feared annexation of populated territory (which the president was leaning towards): "Can we incorporate a people so dissimilar from us in every respect--so little qualified for free and popular government--without certain destruction to our political institutions?", and they might cause the imposition of Catholicism or another single sect in religious war. Or if it they were held as subjects, it would be "the loss of liberty, as it ever has, where free States undertake to hold in subjection extended provinces".
I saw a suggestion, but don't have a source, that northeastern states simply feared more states period as causing a dilution of power. A source lists other Democrats against the war as including Thomas Hart Benton and Albert Gallatin.
(Warning: bits of unmarked irony above)
Well, it's sort of slavery related but for some Northerners the fact that we'd pledged to fight England to guarantee the annexation of British Columbia (54'40 or fight!) meant that by fighting mexico we'd be taking our eye off the ball, so to speak, of gaining the NW, since it is very difficult to fight two wars simultaneously