Very slim.
I'm convinced his pro-life beliefs are genuine. He seems to have a pro-Second Amendment record, but that may be more "Kansas positioning" than core belief. As for illegal immigration, Big Meatpacking in the western part of the state, and small businesses in the east are illegal friendly. Sam can't build a presidential plank on cracking down, cause after he loses, he'll have some 'splainin' to do at the next Senate election.
I really have no reason to believe he would be a bad President. I just don't think he has that Ronald Reagan appeal on camera. We need someone who is willing to say, "There you go again!" - What I mean is, It's OK to nominate a nice guy, But he darn sure better be able to explain and DEFEND conservative ideas.
Which is exactly why Mike Pence needs to be a Republican nominee. He's articulate, he's got the look, and he stand up for what he believes. And he's a freakin' conservative!
But no, they weren't about to elect him Speaker of the House.