In the 27 most competitive seats, most of which President Obama won in 2008, the Republican incumbents trail their opponents by an average of six points, and the pollster predicts two-thirds of those seats will go to the Democrats. But the "second tier" districts aren't as promising for the party, with Republicans leading by an average of nine points in those seats.

Democrats need to win a net of 25 seats for control of the House and are likely to lose between five and 10 seats that they currently hold, so these numbers indicate they'll net a few seats but fall far short of House control.

Obama leads GOP challenger Mitt Romney in these districts by a two-point margin, slightly down from the average by four points he won them by in 2008, and leads by eight points in the 27 "tier one" districts.

The House Republican budget advanced by Rep. Paul RyanPaul Davis RyanMcMorris Rodgers seeks to tamp down unrest Conservative group unveils plan to slash spending by trillion Arizona GOP winner to join Freedom Caucus MORE (R-Wis.) is not well-known yet, but many of its elements are unpopular as framed by Democrats, an indication that they can score some points on the issue. After a ballot test litigating the battle over the issue, Democrats lead by a point in the "tier one" districts, and their deficit narrows from nine to three points in the "tier two" districts.

"To get from serious vulnerability to a wave election, progressives need to make these incumbents pay the price for the positions they have taken," write pollsters Stan Greenberg, James Carville and Erica Seifert.

Healthcare is no longer a problem for Democrats in these districts, as they lead Republicans on the issue by five points. Voters in the districts support increasing taxes on people making more than $250,000 a year by an eight-point margin.

The survey of 1,000 voters was conducted from July 21-26.