The House speaker, John A. Boehner, told a radio host on Wednesday that Republicans should support his plan for a debt ceiling increase because “Barack Obama hates it, Harry Reid hates it, Nancy Pelosi hates it.”

Speaking on “The Laura Ingraham Show,” Mr. Boehner sought to shore up support for his plan, which has come under fire from conservatives and Tea Party members in his caucus.

“The plan we have got on the table is the best opportunity we have to hold the president’s feet to the fire,” Mr. Boehner said. He added that Mr. Obama “wants a $2.4 trillion blank check that lets him continue his spending binge through the next election. This is the time to say no.”

The White House shot back on Wednesday afternoon, using Mr. Boehner’s own words on the radio show to suggest that the Republican speaker was not interested in reaching a compromise with Democrats.

“Time is running out; we need to come together now,” said Jay Carney, the White House press secretary.

“While we don’t all turn into pumpkins on Aug. 2, we do as a country lose our borrowing authority for the first time in our history, and that would be a very bad thing,” Mr. Carney said.