Speaker John A. Boehner says he is gearing up for “a whale of a fight” with President Obama over raising the federal debt ceiling, even though Mr. Obama has repeatedly said he has no plans to negotiate with Congressional Republicans over the nation’s debt limit and wants it lifted without a political showdown.

At an Idaho fund-raiser on Monday for Representative Mike Simpson, a Republican and a close ally, Mr. Boehner said he planned to use the need to raise the debt ceiling to gain political leverage and demand “cuts and reforms that are greater than the increase in the debt limit.”

“The president doesn’t think this is fair, thinks I’m being difficult to deal with,” Mr. Boehner said in his remarks, reported by The Idaho Statesman. “But I’ll say this: It may be unfair, but what I’m trying to do here is to leverage the political process to produce more change than what it would produce if left to its own devices. We’re going to have a whale of a fight.”

Mr. Boehner’s comments came as Treasury Secretary Jacob J. Lew warned him in a letter on Monday that unless Congress raised the debt ceiling, the government would lose the ability to pay all of its bills in mid-October.