The short answer is "With great difficulty".
None of the 15 Slave States is going to vote for him, so he needs all 16 Free States in order to win in the House. This is extremely unlikely.
For him to stand a chance of election, you probably need a PoD well before 1856. Perhaps if the Kansas-Nebraska Act is never passed, and the Republican Party doesn't get formed, then, with the slavery issue on the back burner, he might have a chance of election as a Whig. But even that is a long shot.