Earlier civil war over slavery produces a chance that the specific issues the Whigs campaigned OTL on might still be very relevant in voters' minds after the war is over.I'm going to assume that you are talking about the American Whig Party instead of the British Whigs. Truthfully this is one of the more harder scenarios since the Whig Party was essentially a ticking time bomb (at least in my opinion) due to it suffering from factionalism (Northern Whigs were more anti-slavery than Northern Democrats and the Southern Whigs were more pro-slavery than Southern Democrats) and weak party loyalty. Anyways, if you want the Whig Party to survive then maybe have President Zachary Taylor live so that the Compromise of 1850 is vetoed by him and he then somehow brings both California and New Mexico into the Union as free states which will cause the Southern wing of the party to collapse, with Southern Whigs leaving the party in favor of the Democratic Party, American Party, and Constitutional Union Party, then he loses re-election in 1852 and when the Kansas-Nebraska Act happens (if it still happens) the Whig Party won't collapse since the party is now manily comprised of anti-slavery Northerners and it (maybe?) prevents the creation of the Republican Party.
An earlier civil war over slavery pre-1854 is extremely unlikely, sure tensions were growing between the North and South over slavery after the Mexican Cession and Compromise of 1850, but it wasn't enough to cause a civil war, tensions mainly grew into hostility after the Kansas-Nebraska Act was passed in 1854 (which killed the Whig Party) which would lead to Bleeding Kansas, the formation of the Republican Party, the Supreme Court's ruling in the Dred Scott case, John Brown's raid at Harper's Ferry, the election of Abraham Lincoln, and the Civil War itself.Earlier civil war over slavery produces a chance that the specific issues the Whigs campaigned OTL on might still be very relevant in voters' minds after the war is over.
I would say this is the best path forward for a surviving Whig Party. Harrison's premature death a month into office gave John Tyler the presidency, and Tyler was a really a Democrat who was put on the Whig ticket to appeal to Southern Democrats who opposed Van Buren. With Tyler kept out of the Presidency, a lot of Whig policies would be successfully implemented, which would solidify popular support for the Whigs and allow Clay to run successfully. Past Clay's tenure, I imagine the issue of slavery comes to a head slightly sooner than it did IOTL, but I have no clue how it would go down.Have William Henry Harrison serve his entire term, then be succeeded by Henry Clay. This should be enough to ensure the implementation of the American System, which would help keep the party popular enough to survive even if it still splits over slavery.