The conservative activists say they are dedicated to deposing the lawmakers at the risk of losing seats. Their fervor has only grown after some played a role in the elections of Republican Senate mavericks like Rand Paul of Kentucky, Marco Rubio of Florida and Ted Cruz of Texas over the opposition of party establishment leaders such as Mr. McConnell.

“When you look at the direction Washington, D.C., as a whole is going, when you look at the state of the Republican Party and its decided lack of will to fight, you have to begin looking at the leadership itself,” said Drew Ryun, political director of the Madison Project. The chairman is his father, Jim Ryun, the former Republican congressman and track star from Kansas. “Mitch McConnell is, to me, the essence of the problem in D.C.”

Drew Ryun, who expects the Madison Project to get involved in 14 races in 2014, acknowledged that there were probably easier targets than the Senate Republican leader and two veteran incumbents. “You have to go big or go home,” said Mr. Ryun, who is based in Texas.

The groups do not all jump into the same races. They also have different strategies, with the Senate Conservatives Fund reporting that it has already spent nearly $400,000 on TV and radio advertising in Kentucky. The Madison Project, which has bought fewer ads, is helping with grass-roots organization. FreedomWorks has opened anti-McConnell field offices in Louisville and Lexington.

Republican strategists who have run up against the groups say one of their real strengths is influencing the political dialogue and climate through social media and talk radio, fueling the perception that their targets are in trouble and generating more discussion and news media coverage of their efforts.

The anti-tax Club for Growth, one of the first organizations to take aim at Republican incumbents in an effort to move the party to the right, is not opposing Mr. McConnell. But it has joined the Senate Conservatives Fund, the Madison Project, FreedomWorks and other groups working on Mississippi’s Senate race. They are backing a state lawmaker, Chris McDaniel, in the Republican primary against Senator Thad Cochran, a six-term incumbent and former Appropriations Committee chairman who has showered federal dollars on his state over the years.