(Spencer Platt/GETTY IMAGES)

“The President’s remarks today ignore legislative and economic reality, and demonstrate remarkable irony,” Boehner said in a statement Wednesday afternoon. “His administration has been burying our kids and grandkids in new debt and offered no plan to rein in spending. Republicans have been leading and offering solutions to put the brakes on this spending binge. The President has been AWOL from that debate.”

The statement was the latest salvo in the battle between Congress and the White House on raising the country’s borrowing limit before an Aug. 2 deadline set by the Treasury Department. Senate Republicans and Democrats held dueling news conferences earlier in the day, with each party maintaining its position in the debate. And on Wednesday afternoon the Standard & Poor’s credit rating agency issued a warning that the U.S. risks “selective default” if it misses a debt payment by early August.

Boehner’s charge that Obama has been “AWOL” from the debt-limit discussions isn’t entirely accurate. The speaker and the president discussed the debt talks during a round of golf two weeks ago, and last Wednesday Boehner met secretly with Obama at the White House.

That was one day before House Majority Leader Eric Cantor (R-Va.) announced that Republicans were pulling out of the talks being led by Vice President Joe Biden over an impasse with Democrats on whether tax increases should be included in a final debt-limit deal.

Since then, the House has been on recess, and on Wednesday Obama seized the opportunity to point out that the lower chamber has been “in one week, they’re out one week, and then they’re saying Obama needs to step in.”

“I’ve been here,” he added.

Obama also reiterated Democrats’ call for revenues to be part of a “balanced” deal, while Boehner maintained that House Republicans would not support such a package.

“The President is sorely mistaken if he believes a bill to raise the debt ceiling and raise taxes would pass the House,” Boehner said. “The votes simply aren’t there – and they aren’t going to be there, because the American people know tax hikes destroy jobs. They also know Washington has been on a spending binge for many years, and they will only tolerate a debt limit increase if we stop it.”

As the debt-ceiling debate intensifies, there’s also the question of whether House Republicans may need the support of Democrats to pass a deal. Sen. Charles Schumer (D-N.Y.) argued Wednesday that not including tax revenues in a deal would be a recipe for failure, because no Democrats would back such a plan.

House Minority Leader Nancy Pelosi (D-Calif.), who has consistently called for the repeal of tax breaks for the wealthy and oil and gas companies to be part of a final deal, said in a statement after Obama’s news conference that the president sent the right message.

“Bravo!” Pelosi said. “This is the fight House Democrats have been making for the last six months under the Republican Majority as they move to end Medicare and continue tax breaks for Big Oil. The President has spoken out, and there will be a clearer understanding of what the choices are for the American people.”

She added that House Democrats “join the President in what he has long called for: a balanced, bipartisan package that creates jobs, protects Medicare, and respects the retirement of our seniors and the education of our children.”