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“It’s the last refuge of those who don’t have an argument left,” Mr. King said in an interview. “It tells me that the tea parties have been effective. We wouldn’t have had this debate if it weren’t for the tea parties.”

Following weeks of heated rhetoric against the tea party, a survey by the Pew Research Center found 37 percent of respondents said they had a worse impression of members of Congress affiliated with the tea party movement, while 11 percent said they viewed the group more favorably.

The poll also found that people affiliated with tea parties tended to be twice as engaged in the debate taking place in Washington. About 10 percent of people surveyed by Pew said they contacted an elected official about the federal budget deficit in the past month, but 20 percent of Republicans and Republican-leaning independents who agree with the tea party movement did so.

Mr. King, who voted against the debt deal, said the episode has left tea party groups with “a sense of informed disillusion with the system.” While they changed the discussion in Washington, he said, many are unhappy in the belief that the agreement won’t significantly cut spending.

As for the tea party’s influence going forward, Mr. King pointed to the Iowa presidential straw poll set for Aug. 13, in which he thinks conservative Rep. Ron Paul, Texas Republican and a staunch opponent of raising the debt ceiling, will surprise some observers.

“I think Ron Paul is underrated,” said Mr. King, whose district encompasses western Iowa. “He will show well. If the public doesn’t understand that, it might end up being a surprise to the national media.”