Taylor may still have run with Polk seeking reelection - the Whigs surely would have done everything they could to convince him to run.
The Democrats renominate Polk, but replace Dallas (who has become controversial in his home state due to his role in passing the Walker Tariff) with fellow Pennsylvanian Sen. Daniel Sturgeon. Polk is more well known and popular than Cass, and is slightly more amenable to free soil Democrats than Cass due to his support of extending the Missouri Compromise line to the Pacific - as opposed to Cass's popular sovereignty doctrine potentially extending slavery into Northern territories.
Polk / Sturgeon 45.9 179Taylor/ Fillmore 44.8 111Van Buren/ Adams 9.2 Polk wins reelection. When he dies during his term, Sturgeon is left as president.