The powerful outside group's call came in an email to supporters on Tuesday, shortly after House Republicans announced that they would give up on previous demands for a debt ceiling extension and instead support a clean hike. In the email Senate Conservatives Fund Executive Director Matt Hoskins wrote:
Republicans are giving up because they know that winning is impossible when their leaders are determined to lose. These leaders have telegraphed weakness to the Democrats and sabotaged conservative efforts so many times that Republicans now have no leverage. There's only one solution.
John Boehner must be replaced as Speaker of the House.
Hoskins goes on to warn that Republicans will never have any leverage if Boehner stays as Speaker.
"Unless we install a new leader who will actually go on offense, Democrats will never fear us and we will never have any leverage," Hoskins continued in the email.
The group has previously accused Boehner of aggressively targeting conservatives.
Likewise Tea Party Patriots co-founder Jenny Beth Martin said pushing a clean debt ceiling increase would be a "complete capitulation" by Boehner.
"A clean debt ceiling is a complete capitulation on the Speaker’s part and demonstrates that he has lost the ability to lead the House of Representatives, let alone his own party," Marin said in a statement. "Speaker Boehner has failed in his duty to represent the people and as a result, it is time for him to go… Fire the Speaker."
Asked about the criticism of pushing a clean debt ceiling, Boehner's counterpart in the Senate, Senate Minority Leader Mitch McConnell (R-KY) responded cautiously.
"They're certainly free to express their opinions on what we do here along with everybody else and we'll see how it plays out," McConnell said Tuesday.
This story was updated.