DeMint likes where he is, as a simple Senator with his conservative PAC. From what he’s said before, my take is that he really doesn’t want to run for President, but he’ll do it if he has to. Similar to the leadership positions you mentioned, he doesn’t really want them.
That’s the biggest problem I see with DeMint: he prefers to be more of a behind-the-curtains guy. He’ll raise money and support a conservative candidate, but he’d prefer it to be someone else in those positions.