Obama. The poll also found that two of three voters say it's more important to keep the government open than to block Obamacare.
As House Republicans worry more about a challenge to their right flank than defeat from a Democratic challenger back home, they push their party farther from the mainstream even as their own seats remain secure.
That could complicate the party's efforts to appeal to a greater cross-section of American voters nationally after two successive presidential defeats, veteran Republicans say.
"It's a definite move towards helping make sure that the Republican Party is a regional party that probably controls the House of Representatives for the foreseeable future, but jeopardizes the ability to take back the Senate and the White House in 2016," said former Representative Steve LaTourette, a moderate Republican who retired last year.
Paradoxically, the secure electoral status of Tea Party lawmakers has undercut their party's ability to advance its agenda. House Speaker John Boehner has struggled to keep his party unified on key votes ranging from farm policy to transportation issues to tax increases.
Those Republicans who have defied Boehner most consistently tend to come from districts where Obama only won 35 percent of the vote in the 2012 election, according to an analysis by Binder. Those who have consistently backed him on high-profile votes are from districts where Obama got an average of 43 percent of the vote.
Boehner had trouble keeping his troops in line during the shutdown fight as well. Mindful of the negative fallout his party faced from the last government shutdown in 1995 and 1996, he urged his colleagues to avoid a confrontation.
But his words have carried little weight. House Republicans voted three separate times to pair continued government funding with steps that would weaken Obamacare despite a veto threat from the president.
No matter how the current battle ends, other showdowns - notably the debt ceiling - loom in coming weeks as conservative lawmakers look for additional chances to stand up to Obama.
"There's going to be a number of crises from here all the way to Election Day," Madden said. "This is only one part of all these battles." (Editing by Fred Barbash and Philip Barbara)