A Wednesday meeting between President Obama and House Republicans about the nation’s debt ended with neither side showing a willingness to give ground on any substantive points or rhetorical differences.

Obama is pressing Republicans to agree to a deal that would raise the federal limit on borrowing and curb the growth of the nation’s debt. But in exchange for raising the $14.3 trillion debt limit, Republicans are demanding that the president agree to spending cuts — particularly to Medicare — far larger than he is prepared to accept.

Obama will send Treasury Secretary Timothy F. Geithner to Capitol Hill on Thursday to meet with House freshmen, who have been the most reluctant to raise the debt ceiling and the most insistent on sizable spending cuts. Geithner has said that the government could default on its obligations if the limit is not increased.

Obama and Geithner’s meetings with lawmakers are happening at the same time that Vice President Biden is leading a working group that may represent the best hope for a bipartisan deal. Biden has said that his group will find “well above $1 trillion” in cuts.

Several hours after the White House meeting, House Speaker John A. Boehner (R-Ohio) suggested that the talks were not moving quickly enough to avoid a cliffhanger showdown in early August.

“The issues they’re dealing with have to be dealt with. They are making some marginal progress, but at the rate that that’s gone, we’ll be right up against the wall,” he told reporters in his Capitol suite.

The most dramatic moment of Wednesday’s 75-minute meeting came when Rep. Paul Ryan (Wis.), the man behind the GOP’s budget plan, said Obama is playing politics in the debt debate. He accused the president of mischaracterizing the GOP budget proposal as turning Medicare into a “voucher” program that would hurt seniors. Ryan’s comments earned him a standing ovation from his colleagues.

“It’s been misdescribed by the president and many others,” Ryan said at the White House after the meeting. “I just said . . . that if ‘we demagogue each other at the leadership level, then we’re never going to take on our debt.’ ”

According to people familiar with the meeting, Obama replied that both sides have demagogued the debt issue. He told the Republicans that they’ve been guilty of playing politics, too, with their attacks on the “job killing” health-care law.

Obama told Ryan that he thinks the congressman is sincere but that the two parties have fundamental philosophical differences. He said that the Republican plan to restructure Medicare would not bring down the cost of treatment but instead shift costs to seniors.

“Compromise needs to be a two-way street,” Obama said. He said that with age, he has increasingly come to know that there are good arguments on both sides of an issue.

The president’s meeting with Republicans came after the House voted overwhelmingly Tuesday against raising the debt ceiling. Republicans held the vote to show that Obama doesn’t have support for his position that the limit should be increased regardless of whether spending is reduced.

After the meeting, Republicans demanded that Obama agree to spending cuts equal to or greater than the increase in the amount of debt that he wants to fund government operations. Covering U.S. obligations through 2012 would require about $2.4 trillion in borrowing.

Boehner said that negotiations in the Biden group should conclude in about a month and that eventually he and Obama need to be more directly involved in the talks. “The president could engage himself. I’m willing. I’m ready. It’s time to have the conversation. It’s time to play large ball, not small ball,” the speaker said.

White House spokeswoman Amy Brundage said late Wednesday that Obama is monitoring the Biden talks. “Both parties acknowledge that the group is making progress and talks are productive,” she said.

Republicans remain particularly upset that Obama invited Ryan and Rep. David Camp (Mich.), the chairman of the Ways and Means Committee, to a speech at George Washington University on the federal debt — only to make “some pretty outrageous claims” about Ryan’s budget plan, Boehner said.

Staff writer Bill Branigin contributed to this report.