Before his death, Tyler was planning to send Federal troops to Santa Fe to defend the jurisdiction of New Mexico Territory against the State of Texas, which claimed the land and was sending Texas Rangers to enforce its claim. I've read a couple historical authors (not professional historians, I don't think) who say that would've escalated into an early Civil War had Tyler not died.
I've also read other people who've speculated the rest of the South wouldn't have stood behind Texas in a showdown, but that's at least a possibility.
I've also seen speculation on here that he was planning on vetoing the Compromise of 1850, since he was opposed to slavery spreading to the Southwest. If that had happened, there's certainly a potential for violence.