There's a non-zero chance that him living on could have led to an earlier Civil War. Though a slaveholder himself, by the time of his death his strongest ally in Congress was William Seward, who was generally considered to the leader of the anti-slavery wing of the Whig Party. Taylor's key policy was that California and New Mexico should immediately gain statehood without regard to the status of slavery. This angered Southerners since both were widely expected to become free states, and also because his stance denied the expansive land claims of Texas, which was a slave state.
Irl his policies in part led to the
Nashville Convention, which represented the first time since 1815 that major state leaders seriously contemplated secession. A mini-realignment occurred in the South for the 1850 and 1851 election cycles, but the victory of pro-Compromise Democrats and Whigs temporarily ended talk of secession.
If Taylor had lived, its certainly possible that no compromise would have been reached, and that Southern states would have begun to secede during his presidency. Alternatively, the absence of the compromise could have led to further sectional polarization and the outbreak of civil war after the 1852 election.
