The chart above was made from information provided in a recent Pew Research Center survey (conducted between October 9th and 13th of 1,504 nationwide adults, with a 2.9 point margin of error). It gives a demographic breakdown of how various groups would vote for their House representative, if the vote was taken now. Note that most groups now support Democrats. One particularly telling statistic is that while men are evenly divided, women favor Democrats by 12 points (which should make Democrats happy, since there are more women voters than men to begin with).
And this is not the only poll that shows this leaning toward Democrats. In fact, it has gotten so apparent that the prestigious Cook Political Report has moved at least 14 seats from the Republican column to the Democratic column -- and the Democrats only need 17 seats to flip the House. While the effective gerrymandering done by Republicans in 2010 will save them many seats, it cannot save them all. It's just an impossibility to gerrymander every seat into a safe one, and there are at least 24 seats deemed competitive nationwide.
Part of the reason for this dramatic shift toward Democrats is the government shutdown, which the public rightly blames Republicans for. But this is really something that has been slowly building for months now, as people are finally starting to realize the Republicans are only interested in protecting the rich -- not in fixing the economy or helping Americans still hurting from the recession. Consider the charts below, which contain some other reasons why people are preferring Democrats these days (from the same Pew survey).