Democrats had a chance to when they controlled both, and they didn't. This problem may not be as partisan as you think..
Due to the way contemporary news media works, I think that Democrats (for the time being) have rapidly depreciating political capital after any election. Last time they regulated health care, despite knowing it would cost them many seats in the coming election. To say that 'they had a chance' I think ignores a few important facts about the contemporary US electorate.
Democrats controlled both for a very short amount of time. Al Franken was part of their majority but had his membership delayed by a recount. Ted Kennedy then died and his seat went to a Republican. They never actually had a true supermajority.
That's exactly right. This is why we need to collaborate across party lines.
I think you might want to run that thought through followthemoney.org