Being a Palmer on 24 is like being Cersei Lannister on Game of Thrones. You'll gain power, but almost certainly suffer horribly in the end. President David Palmer was assassinated in the opening minutes of Season 5, and by the end of Season 6, his brother Wayne—who had also become President—was in a coma following injuries received during a terrorist bomb blast. The show never came out and said whether Palmer survived his coma, instead focusing on his Vice-President assuming duties and then losing the election to someone else.
Actor D.B. Woodside, who portrayed David Palmer, doesn't think his character's dead. As he said to IGN, "Anybody who watches 24 knows that the characters…constantly kind of go away, maybe for a year, come back, go away, come back—unless they're dead. So…Wayne Palmer does not die. That's what I can say, is he's not dead, so we'll see. We'll see what happens."
Unfortunately, what happened was the show ended, got rebooted, then ended again, and we didn't hear anything about Wayne Palmer. He may have recovered from his coma, he may still be comatose, or he may be as dead as his brother. Considering the stuff other characters on that show have survived, Wayne's chances of making the next reboot (should that happen) are probably better than slim.