First of all, Obama wouldn't fight. He would try to make a deal with them to stay in office and represent the invading force. Second, every chicken shit liberal in the country would follow along right behind him, the way they do now. The only ones who would fight would be the REAL Americans, the ones that value their freedom and independence. That leaves out every liberal parasite in this country.
Conservatives, libertarians, and independents would wage a guerilla war against the Chinese or Russians (whoever) and the sniveling liberals would be the informants, snitching on them to curry favor with the invaders. They're boot lickers right now for Obama, why would anyone think they would suddenly grow balls if somebody ELSE came in and took our freedom away?
Calm down. First of all, there would be no need for a guerrilla war because the US military would crush any such invasion in very short order. Second, most democrats would also stand up and fight if the homeland were being directly invaded. Don't let partisanship make a fool of you. Only the most ridiculously extreme on either the left or the right (and yes we have some such assholes here, unfortunately) would refuse to defend the homeland out of partisan spite. The nonsense that gets posted here is just that - nonsense. If push came to shove, the word games and banter would be put on hold and the vast majority of able-bodied American men - and women - would take up arms, or a knife, a bat, a pointy stick, or just their bare hands and show the visitors what a warlike people is REALLY like.