I'd say it's reasonable to imagine that he'd back the southern / slaveholding view rather consistently. Indeed, he might have authored the majority opinion in the Dred Scott case. Had the Compromise of 1850 or the Kansas-Nebraska Act been brought before the Court, I could imaging Buchanan opting for the Court to hear either or both, and voting (again) on the pro-slavery side.
As to the Dems' nominee in 1856: Breckenridge might have been able to get the nomination, albeit grudgingly (Northern Dems wouldn't have cared much for the choice), and he surely would have had to have a northerner (perhaps Stephen Douglas?) as his running mate. I'm not sure the time was right for Douglas yet, unless he chose a no-nonsense southerner like Jefferson Davis as his running mate.
Breckenridge might have beaten Frémont, but it would have been a nail-biter of an election. With a Douglas / Davis ticket, it's possible just enough people might have voted for a Free Soil candidate to throw the election into the House, whereupon the fun really starts, especially if Douglas is able to muster enough support to win. That would probably result in four years of gridlock, and essentially the same results for the 1860 election as in OTL.