Speaker John A. Boehner of Ohio said on Wednesday that his conference does not have a problem raising taxes on the rich in theory, but they simply will not accept doing it by raising tax rates.

Instead, he said the conference wants to limit deductions for those with high incomes.

“The revenues we’re putting on the table are going to come from, guess who? The rich. There are ways to limit deductions, close loopholes and have the same people pay more of their money to the federal government without raising tax rates, which we believe will harm our economy,” he said. “Our members believe strongly that raising tax rates will hurt the economy. Closing loopholes, especially on those that are wealthy, is a better way to raise this revenue than raising rates.”

Boehner also called on President Barack Obama to send another offer to Congress. The two sides traded offers, with the White House sending an offer last week and House Republicans returning a counteroffer on Monday.

“Frankly, it was the balanced approach that the president’s been asking for,” Boehner said of the GOP offer. “If the president doesn’t agree with our proposal and our outline, I think he’s got an obligation to send one to the Congress, and one that can pass both houses of Congress.”

GOP aides said the two sides have not been negotiating and Boehner and Obama have not spoken in a week. The House will recess today, but Boehner said he is not leaving. “I’ll be here and I’ll be available at any moment to get serious with the president,” he said.

Majority Leader Eric Cantor, R-Va., meanwhile, called on Democrats to look at spending cuts and entitlement reforms, rather than just taxes, which he called an “obsession” for the party.

“We have got to do something about the spending. An obsession to raise taxes is not going to solve the problem. What will solve the problem is doing something about the entitlements, taking on the wasteful spending in Washington,” he said.

His comments are the mirror image of what Democratic leaders have said about Republicans, namely that they are fixated on cutting spending and changing the entitlement system but are vague about where tax revenue will come from.