In a survey of 24 seats, Republicans fall behind in 17 head-to-head matches against “generic Democrat candidates” among registered voters and lag in an additional four districts when respondents are told the Republican candidate supported the shutdown, according to the surveys by Public Policy Polling that were funded by the liberal group, MoveOn.org

Democrats would need to pick up 17 seats to take over the House — something the polling reveals could be within reach.

One district that shows a favorable position for a Democratic challenger is New York’s 19th Congressional District, the high-profile contest in which Sean Eldridge, the husband of Facebook co-founder and New Republic owner Chris Hughes, is looking to unseat the Republican incumbent, Chris Gibson. However, Eldridge’s name does not appear on the survey as the challenger.

The other 16 House Republicans who trailed even when the poll didn’t mention the shutdown: California’s Gary Miller, Colorado’s Michael Coffman, Florida’s Steve Southerland and Bill Young, Iowa’s Tom Latham and Steve King, Illinois’ Rodney Davis, Kentucky’s Andy Barr, Michigan’s Dan Benishek,Tim Walberg and Kerry Bentivolio, New York’s Chris Gibson, Ohio’s David Joyce, Pennsylvania’s Pat Meehan and Mike Fitzpatrick, and Wisconsin’s Sean Duffy.

The poll also found that a majority of respondents opposed the government shutdown as a means to “to stop the health care law from being put into place.”

The 24 state surveys were conducted Oct. 2 to Oct. 4 and with sample sizes ranging from 600 to 700 voters.