Speed and stealth is everything, and it is one thing the US is very good at still. It is very likely that NATO would win any race to critical transit points in eastern Ukraine even if Russia received word just as NATO forces did. As long as lightly armed US troops are physically controlling key roads and transit passes, it would mean that Russia would have to shoot them to get by. Since that would likely be unacceptable to Russia for obvious reasons, it's the only real way to insure no Russian invasion. The problem is that it risks nuclear war, which is something that Putin has proven willing to do in Crimea (and Russia also did in Kosovo). But Russia has a lot more at stake in the Ukraine than the US does, so I think it is unlikely we will see Obama agree to that kind of gamble.