Actually, I think the Republicans' platform resisted the EXPANSION of slavery (primarily into Kansas and Nebraska Territories). They were less strident in their criticism of the existing institution, although certainly more grounded in their opposition than the Whigs had been. Lincoln, for example, never ran on an abolitionist platform, even though his newly formed Republican Party was founded or encouraged by the William Lloyd Garrisons of the era.
More important, though, any "free soil" president---and Lincoln was the first---would be able to override the pro-slave regimes in the South by appointing anti-slave federal judges, marshals, customs inspectos, and postmasters. This was critical, and everyone knew it. From 1836 on, only having a "northern man of southern principles" in the White House prevented war, and thus the Dems intended to keep the White House, which they did, except for two weak Whigs who had no intention on acting on slavery.