(CNN) - Tea Party Republicans have been flexing their muscles in the debt ceiling standoff, but their strong-arm tactics could backfire if the public comes to view them as unrelenting extremists.
John Boehner has been struggling to control the Republican House, and has been pushed and pressured into a debt ceiling bill that's left little room for compromise - and the Tea Partiers have been the ones doing the pushing.
They're a relatively small but very powerful group of Republicans.
"The Tea Party has forced Speaker Boehner more to the right. That involved deeper spending cuts and also support for the balance budget amendment. So they have had a disproportionate impact on the entire Congressional debate," Darrell West with the Brookings Institution said.
It's extraordinary considering the portion of the House they make up. The Tea Party Caucus has 60 members, which is only a quarter of the total number of Republicans in the House.
But when Boehner had to delay the vote on his bill to get more votes, Tea Party members made up more than half of the Republicans who were prepared to vote no.
It's a continuation of the moment triggered last fall when the Tea Party captured political lightning in a bottle and helped elect dozens of new congressmen. They came in on a promise to shock Washington into spending less and cutting more.
Their unwillingness to compromise has changed the way the government handles its debt.
But now even Senator John McCain, a budget-hawk himself, said they risk over-reaching if they never compromise.
"That is not fair to the American people to hold out and say we won't agree to raising the debt-limit until we pass a balanced budget amendment to the Constitution. It's unfair, it's bizarro," McCain said on the Senate floor.
The Tea Party may already be setting itself on a road to self-destruction.
"They are now putting themselves in peril. The Tea Party could destroy itself, if it is now careful, if it is seen as taking us into default," CNN Senior Political Analyst David Gergen said.
Public disapproval for the Tea Party has been steadily growing, from 26 percent to 47 percent, since January last year. Analyst Darrell West said that may not hurt Tea Party congress members themselves in their next elections because many come from safe districts.
But he said the Republican Party may suffer the consequences.
"The Republican presidential nominee may end up suffering the consequences, because Obama certainly is going to tie that GOP nominee to the more extreme elements within the Republican party in Congress," he said.
But many Tea Party lawmakers seem to relish the fight, and said voters sent them to Washington on a mission, and they're more worried about cutting spending than winning a popularity contest.
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