Tea Party leaders are claiming victory in the outcome of the debt ceiling talks despite indications that their tough tactics, which pushed the US to the point of a government shutdown, may have alienated many moderate voters. Key players in the Tea Party movement said that for the first time they had succeeded in putting spending cuts at the centre of Washington affairs.

"We defined the contours of the debate and made it impossible to raise the debt ceiling without achieving serious spending cuts," said Phil Kerpen, head of policy at the prominent Tea Party group, Americans for Prosperity.

Kerpen estimated that of the 66 Republicans in the House of Representatives who voted against the final compromise, on the grounds that it does not cut public spending enough, about a half were Tea Party affiliated. The group included Michele Bachmann, a candidate to be the Republican presidential nominee.

One of the few points that both sides in the bitter talks can agree upon is that the Tea Party was seminal in shaping the terms of the debate.

Though the movement has been relatively quiet since its impressive showing in last year's midterm elections, the lull was deceptive – as the impact on such a crucial confrontation in Washington shows.

Newt Gingrich, who led the Republicans in their last major clash over spending in the 1990s, credited the Tea Party with having beaten Obama.

"A very leftwing president blinked, and that would not have happened without the Tea Party," he told Fox News. A similar recognition of Tea Party power was expressed from the left of the Democratic party, though in more impassioned language.

Vice president Joe Biden was forced into damage limitation mode after it was reported that at a private meeting he had convened with Democratic Congress members, Tea Party supporters were accused of "acting like terrorists".

Sal Russo, an influential strategist and founder of the Tea Party Express, said that even the terrorist jibe was a sign of success. "When people make outrageous comments like that you know they have lost the rational debate and you are winning."

The messy nature of the partisan fighting over raising the debt ceiling carries risks for the Tea Parties.

The more influence they wield on Capitol Hill, the more they will be held accountable for the impact of their actions.

That is already reflected in opinion polls. A survey by the Pew Research Center found that 37% of respondents had formed a less favourable opinion of the Tea Party affiliates in Congress as a result of the debt ceiling standoff – exactly the same indication of political damage as recorded for Barack Obama.

The only group that fared worse was the Republicans in Congress, who suffered a deteriorating reputation among 42% of the survey sample.

Pollster Scott Rasmussen, co-author of a book on the Tea Parties, Mad as Hell, said that he expected to see a backlash against the movement following all its recent activities.

"Among Democrats, many voters already have negative feelings and that may grow among moderate Republicans and unaffiliated voters."

But Rasmussen added that as an authentic grassroots movement, the advance of the Tea Parties would not be halted.

"The ideas that animated the Tea Parties will continue to grow regardless of what happens to their popularity."