Whether or not an Obama presidency would be in keeping with Catholic teachings is a no-brainer question -- of course not, based on his well-established 100% support for abortion on demand, even to the point of refusing to require medical attention for babies who survive abortions. The pro-abortion policies as well as the judicial appointments from an Obama administration would be with us for decades to come.
But...
The question of "whether Catholics can stomach a Barak Obama presidency" is a different question, I think. A reading of Romans 13:1-6 and 1 Peter 2:13-17 should shed some light on the matter. The Church teaches as sacred scripture demands that "every soul submit to the existing authorities, since there is no authority except from God."
In fact, Saint Peter tells us in scripture that we should do so "for the Lord's sake" and it is God's will that by doing right we should put to silence the ignorance of foolish men. "Live as free men, yet without using your freedom as a pretext for evil."
So, yes, assuming a legitimate, free and fair election, Catholics would indeed be able to stomach an Obama presidency.