In House and Senate races across the country, many of the traditional and influential centers of power within the party are taking sides in primaries, overwhelming challengers on the right with television ads and, in some cases, retaliating against those who are helping the insurgents. In Mr. Black’s case, one by one, powerful Republicans started backing his rival, Barbara J. Comstock, a member of the State House of Delegates. First Mitt Romney endorsed her. Then came Citizens United and the president of Americans for Prosperity, the group financed by the wealthy Koch brothers.

A few day after he announced his candidacy, Mr. Black dropped out. “It was pretty evident that she had all the machinery,” he said in an interview.

One of the biggest challenges for Republican leaders in the 2014 midterm elections will be how to hang on to the Tea Party support that has been so instrumental to the party’s growth, while winning back voters alienated by hard-right candidates. These conflicting goals were evident last week as Speaker John A. Boehner of Ohio shelved plans to tackle immigration reform in the House, bowing to pressure from conservatives.

“We’re not picking a fight with the basis for the Tea Party,” said Scott Reed, the senior political strategist for the U.S. Chamber of Commerce, who noted that most Republicans were sympathetic to the free-market, small-government philosophy that inspired the movement. “But some have hijacked the Tea Party model and taken it to an extreme level.”

The chamber has become one of the establishment’s most powerful forces this year by taking the highly aggressive step of working in primaries to defeat Republicans who are seen as unelectable and damaging to the national party.