Yes, they had held a narrow majority in the House until the last election. As demonstrated by the vote yesterday, just because you have a majority doesn't mean you will pass what legislation you bring up.
Barney is, and was, a very powerful member of Congress and has been an ardent supporter of Fannie and Freddie for many years. There is absolutely no way any meaningful legislation was going to get approved unless Barney was on board or the Republicans had a much larger majority. Neither was realistically going to happen.
Should the miraculous have happened, and all the Republicans in the House voted for it; how exactly would it have gotten through the Senate? It wouldn't have, and the cries would have gone out about how the mean Republicans were trying to keep minorities from being able to get their share of the American dream.