I've got him doing so in my "Daniel Webster as Harrison's VP" TL that is close enough to ready to start that I might do it soon. A 7-way

eek

election free-for-all comes in 1852, but that's from thigns set in motion earlier.
Essentially, if Taylor chooses the Democrats, in my view, it's likely because the Whigs' Southern faction feels left out by some Webster snobs, as the party is pushed too far toward teh Free Soil camp. Since taylor did have some things in common with the Democrats he'd have probably willingly bolted, but you'd need an unpopular Democratic president in 1844, which could happen if Popular Sovereignty becomes a huge enough issue.
The Whigs were a loose band of people held together by men such as Henry Clay. They might run Clay just because they don't have anyone else, or Scott, but either way, if the Democrats have won a war, they'd still be the party in power, just the President would be able to be "thrown under the stagecoach" (no buses yet

) and blamed for all the problems. While Taylor gets credit for all the success. So, I think Taylor wins no matter who runs for the Whigs.
If a Whig is PresidentI doubt the Mexican-American War happens, though I suppose it's possible.
(Maybe I'll start it soon - I usually dont do really detailed TLs, this will be about like "Created Equal," if I do.)