If he isn't having sex with her then I fail to see the problem.
Cohabitation isn't sinful, sex outside of marriage is sinful. BTW, you don't have to cohabit to have sex.
BTW, Christians sin, but Obama seems to want to put being a politician as a priority to his relationship with God. He doesn't seem to want Christian ideals to interfere with his duties as Commander in Chief.
Maybe you can't be a politician AND a Christian, BTW I think the same of Nancy Pelosi, who's supposedly Catholic and others.
I'm also not sure of Republican politicians.