“I do think it is going to be more competitive,” said Jenny Beth Martin, a co-founder of the Tea Party Patriots. “With the freshmen who claim to be Tea Party or claim to support the ideas of the Tea Party movement but haven’t kept their promise, I think it will be tough for them.”

Ms. Martin said she regularly fields e-mails from New York Tea Party groups, as well as others in Georgia and Mississippi, complaining about freshmen House members who voted for a disappointing short-term spending agreement with President Obama that fell short of the party’s budget-cutting goals. “They have broken their promises,” she said. “People are dissatisfied.”

Among the potentially vulnerable members of the class of 2010 is Mr. Farenthold, whose victory was so unexpected that the national party more or less ignored him during the campaign. His race also was so close — he won by 799 votes — that it was called just before the new Congress convened in January. He got the last office available, the palatial space once enjoyed by the senior Democrat he ousted, Solomon P. Ortiz, who had held the seat for nearly 30 years.

Mr. Farenthold, a wealthy former radio talk show host and computer consultant, is known on Capitol Hill less for his legislative prowess than for his frequent cable TV appearances on MSNBC and his rather non-businesslike tweets that began long before he won (examples: “I like pizza but it doesn’t like me” and “Let’s not forget Israel is our B.F.F. in a hostile area”).

Mr. Farenthold said that he goes on MSNBC because he is asked to and because it is more like “missionary work” than going on Fox News, and that his use of social media is part of who he is. “Twitter scares the daylights out of my office staff,” he said. “But social media is not just another avenue to put out your press releases. It’s got to have a little edge.”