Obama won't get impeached if he moves forward with his plans for Syria. He will get a pass, and not "because he's black" either. No President is getting impeached for legally using his Presidential power. As long as he keeps any attack under 90 days, he is within his boundaries, even without Congressional approval.
What is more interesting is what is going on in Congress. Where are all of my anti-war Democrats? What happened? How have they become so bloodthirsty?
Obama is pushing for this simply because he made a bad statement back in 2012, when he made his initial "red line" comment, and the White House aides confirmed it on the second day. Claiming now that it is an "international red line" is a joke, as none of our main group of allies are looking to take action - making this a unilateral action.