Story highlights Poll conducted after government shutdown shows small majority think GOP control of House is bad

Results are first time since GOP took control of House in 2010 that more oppose its control

More than six in 10 say Speaker of the House John Boehner should lose his job

Obama's approval numbers didn't take same hit that GOP's did after shutdown

Just over half the public says that it's bad for the country that the GOP controls the House of Representatives, according to a new national poll conducted after the end of the partial government shutdown.

And the CNN/ORC International survey also indicates that more than six in 10 Americans say that Speaker of the House John Boehner should be replaced.

The poll was conducted Friday through Sunday, just after the end of the 16-day partial federal government shutdown that was caused in part by a push by House conservatives to try and dismantle the health care law, which is President Barack Obama's signature domestic achievement.

According to the survey, 54% say it's a bad thing that the GOP controls the House, up 11 points from last December, soon after the 2012 elections when the Republicans kept control of the chamber. Only 38% say it's a good thing the GOP controls the House, a 13-point dive from the end of last year.

This is the first time since the Republicans won back control of the House in the 2010 midterm elections that a majority say their control of the chamber is bad for the country.

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CNN Chief National Correspondent John King said there is time for Republicans to recover before the 2014 midterms.

"The midterm election is a year away. There's plenty of time for Republicans to work on the brand, but they've taken a bit of a beating here. They've got some work to do. They need a bit of a makeover," King said.

Majority want Boehner out

"We fought the good fight. We just didn't win," Boehner said at the end of the shutdown. And while he received a standing ovation at a closed gathering of House Republicans as the crisis came to a close, he may not see anything to applaud in the new poll.

"John Boehner fares just as badly as the GOP," CNN Polling Director Keating Holland said. "Sixty-three percent of all Americans think that Boehner should be replaced as Speaker of the House, a view shared by roughly half of all Republicans."

According to the poll, only 30% of the public says Boehner, who became Speaker in January 2011, should continue in that role.

Congress near historic lows

The survey indicates that the approval rating for Congress remains near an all-time low. Only 12% of those questioned say they approve of the job Congress is doing, just two points higher than the historic low in CNN polling. And 86% give federal lawmakers a thumbs-down, also near the all-time high.

Forty-four percent say they approve of the job the President is doing with 52% saying they disapprove.

"Barack Obama's numbers are pretty anemic, but he remains in much better shape than the GOP," Holland said. "Even though Obama's approval rating remains stuck in the mid-40s, it didn't take a hit during the shutdown -- 44% just before the shutdown began; 44% now."

According to the survey, 44% also say they have more confidence in Obama rather than the GOP in Congress to deal with the major issues facing the country today, a 5-point drop from last year; 31% say they have more confidence in congressional Republicans, unchanged from last December.

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"The biggest change on that question is the 21% who volunteer that they don't have confidence in either side -- a remarkably high number that is roughly double its usual level," Holland said.

Majority favor health care law or say it doesn't go far enough

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Even though they lost this round, conservatives vow to continue their fight to dismantle Obamacare. And they point to major troubles with the rollout of the website where Americans without insurance can enroll in the new health care exchanges.

The president addressed the debacle at an event Monday at the White House, saying there was no way to sugarcoat the issues that applicants have experienced.

According to the poll, just more than four in 10 say they favor the law, with 56% opposed to it.

But of those opposed, 38% say they are against the law because they think it's too liberal and 12% say it's not liberal enough. That means that 53% either support Obamacare, or say it's not liberal enough.

The health care numbers are little changed from late last month, just before the start of the shutdown.

The poll was conducted for CNN by ORC International, with 841 adults nationwide questioned by telephone. The survey's overall sampling error is plus or minus 3.5 percentage points.