Don't forget Tyler was sufficiently ill thought of to have impeachment seriously proposed. Theodore Roosevelt called him "a man of monumental littleness" and from what I've been able to glean, TR was right. Hence, I don't know that Tyler's run would have been much more than a sideshow--or if it had been, it would have damaged the pro-slavery cause (recall that Tyler was sufficiently so that he stood for the Confederate Congress and was elected, but died in early 1862 before he could take his seat) by dividing it into pro- and anti-Tyler factions. That could have perhaps accelerated statehood for Kansas, scuttled the Compromise of 1850, and perhaps advanced the Civil War a handful of years--which would have probably meant a quicker northern victory. Then we'd be hailing (perhaps) president Frémont or Seward as the savior of the union and the man who (speaking somewhat loosely) ended slavery.