Unhappiness but allowing it to pass is the likely course. It was the Missouri Compromise that REALLY bought the free-slave debate into the limelight of national politics (even if it was clearly shimmering before then).
Assuming a parallel course to OTL after the Compromise I'd see more Mexican territory taken, maybe West Florida split off as a third state to MS and AL when they do get statehood (West Florida is admitted out of the combined AL-MS coast and the inland areas kept as two separate territories until their statehood), and Texas divided up as needed (two states at the least, certainly). The Republic of Sonora and its secondary portion of Baja California will also get much more support by filibusters as potential balancing slave states. Hell, maybe Virginia will be egged on by fellow southerners to allow West Virginia secession if local elites agree to become a slave state despite the poor white farmers not owning much of any.
So at the least an extra Texas state (we'll assume that "Lincoln" proposal I suppose?), a Baja California and Sonora state for an extra two, possibly an earlier officially slaver West Virginia, maaaaaybe a West Florida state. So that's at least five in addition to all OTL ones by the Civil War.
Basically, the south will be even more expansionist for sure, and maybe a bit more divide-happy.