It's quite conceivable that the complicated negotiations which lead to the Compromise of 1850 IOTL could go off the rails. They very nearly did, after all. If no compromise is reached, it's possible that the South will secede. However, the result will be very different than it was IOTL, for the White House would have been occupied by a Democrat with Southern sympathies rather than a Republican determined to hold the Union together.
Who was, nonetheless, an uncompromising Unionist.
It was difficult enough to get any states other than South Carolina and Mississippi to declare secession in 1860-61, even with an openly anti-slavery President-elect from the North.
Getting such declarations passed when the President is himself a Southern slaveowner would be all but impossible.
If somehow that happened, Taylor would immediately march against the seceding states to enforce Federal authority. As there would be not the slightest possibility of his being perceived as anti-Southern or anti-slavery, save by the most demented Fire-Eaters, there would be no effective resistance.
But let's try for the AHC:
0) Polk sends a replacement for Trist to negotiate peace with Mexico. The substitute has instructions to demand a lot more, and gets it. The border runs from the Rio Grande about 150 km south of El Paso to the Pacific, and the US gets Baja California.
1) Taylor comes down sick in the last days of the Mexican War, and dies.
2) In 1848, the Whig Party nominates Daniel Webster for President, with Winfield Scott as VP. (Scott is from Virginia.)
3) Webster-Scott wins.
4) However, due to butterflies, no one finds gold in California until 1853.
5) Meanwhile, a bitter dispute arises over the organization of the Mexican Cession. The "36-30 line" is extended to the Pacific. Many anti-slavery Northerners are offended, especially by the extension of slavery into previously free Mexican territory. Many Southerners are offended by the failure of Congress to pass a Fugitive Slave Act. California is divided into two Territories.
6) Webster dies, and Scott becomes President in 1852.
7) President Scott re-nominated by the Whigs, with [some Northern Whig] as his running mate. This man "Smith", though no one much knows it, is becoming strongly anti-slavery. Scott wins narrowly.
8) 1853: gold discovered in Northern California. The Rush is on!
9) 1855: Northern California statehood becomes an issue. Also, there is talk of a transcontinental railroad. Douglas cuts a deal with the South - repealing the ban on slavery in Territories north of 36-30 in return for a northern railroad route. VP Smith casts the tie-breaking vote against the Douglas bill, and then makes a flaming anti-slavery speech. However, a few days later, the bill is brought up again and passes.
10) Pro-southern militants try to seize control of Northern California. Thousands of southern "Carpetbaggers" go west to assist (and get rich). Scott, worn out by the stressful Presidency, dies. Smith becomes President and orders the Army to suppress the Carpetbaggers. He continues to denounce slavery. There is anti-slavery agitation in Sonora Territory, which Smith supports.
11) The election of 1856 sees a grand realignment: southern "Cotton Whigs" join the Democrats while northern "Free-Soil Democrats" join the Whigs. Smith wins re-election with 55% of the popular vote and a narrow majority of the electoral vote (150 of 293 - all in Northern states).
12) Following the election of a "sectional", "abolitionist" candidate, the Deep South states declare secession, followed by the Upper South after Smith proclaims a state of rebellion and calls for troops. The war is on by December 1856.