As Monday’s White House budget talks got down to the nitty-gritty, Eric Cantor proposed a series of spending cuts, one of them aimed squarely at college students.

The House majority leader, who did most of the talking for the Republican side, said those taking out student loans should start paying interest right away, rather than being able to defer payments until after graduation. It is a big-ticket item that would save $40 billion over 10 years.

At one point, sources say, President Obama pushed back against the mounting menu of spending cuts while the tax column on the negotiating sheets remained blank. He asked the Republican leaders how they expected him to take their proposals seriously.

“I’m not going to do that,” Obama said. “I’m not going to take money from old people and screw students,” not without some compromise on the tax-increase side.

The talks made little progress, which comes as no surprise given the dueling press conferences that preceded the afternoon session. But the impasse brings the federal government one day closer to the August 2 deadline, when it would plunge into default if Congress doesn’t lift the debt ceiling.

There is a mounting sense of frustration at the White House, as the two sides seem to be talking past each other. Most insiders believe that at best the two parties will have to cobble together a modest deal that avoids default but falls far short of the large-scale agreement that Obama and House Speaker John Boehner briefly thought they could achieve.

Republicans are resisting not just tax increases but significant cuts in defense spending, the sources say.

Officially, the day was spent reviewing the spending cuts tentatively agreed to during earlier negotiations led by Vice President Biden, which amount to $1 trillion to $1.5 trillion. But that level falls short of Boehner’s original demand that the Democrats agree to spending cuts equal to any hike in the debt ceiling.

The president has offered to negotiate substantial cuts in Medicare and Medicaid, but only if the GOP gives ground on revenue increases, including breaks for his now-standard litany of oil companies, corporate-jet owners, hedge-fund managers, and millionaires and billionaires.

Obama returned to this theme in the talks, saying everyone is being asked to sacrifice except rich people. The Republicans repeated their belief that any tax increase would damage the fragile economy.

At a morning news conference, the president vowed not to sign a short-term fix of up to three months or perhaps even six months. Administration officials say the declaration reflected not just a desire to boost pressure on the Republicans, but Treasury Secretary Tim Geithner’s concern that the markets would be spooked by a temporary deal that would force Washington to confront the same issues early next year.

In his morning session with reporters, Obama also delivered a tough message to his party by saying many of its lawmakers “would prefer not to have to do anything” on Medicare, Medicaid, and Social Security. He positioned himself as the reasonable adult trying to bring his squabbling charges together.

The Huffington Post reported that the president has offered to phase in an increase in the eligibility age for Medicare from 65 to 67—but only if the GOP gives ground on tax issues.

Obama attempted to neutralize Republican arguments about raising taxes in a weak economy by noting that no increase would take effect until 2013.

If Obama’s goal was to move GOP leaders toward his position, he failed.

At his own news conference, Boehner said: “The president and I do not agree on his view that the government needs more revenues through taxes on job creators. The president and I also disagree on the extent of the entitlement problem and what is necessary in order to solve it.”

The speaker also reinforced his original demand in the talks, saying: “The House can only pass a debt limit with spending cuts larger than a hike in the debt limit, as well as real restraints on future spending.”

At a separate session with reporters, Cantor said Obama had proposed $1 trillion in tax increases during a White House meeting on Sunday night. “Our members did not come here to raise taxes,” Cantor said. “In fact, we went and pulled the Pledge to America, and in the Pledge to America, sprinkled throughout is our pledge not to raise taxes on the American people.” The pledge was the party’s platform in the midterm elections.

Asked if Boehner might agree to a deal that he could not support—the two GOP leaders split over the weekend over the size of a potential agreement—Cantor said, “No, I think we are on the same page. I know you all love to write the soap opera here. And it is just that; it is something that I think belittles the real question here and that is the difference between the sides and that is between the fact that Barack Obama wants to raise taxes and Republicans don’t.”

As their rhetoric makes clear, the two sides at this point are engaged in a game of repetition rather than true negotiation. Obama has the bigger megaphone, but with their control of the House, the Republicans essentially have veto power. The president acknowledged as much, saying that if each side takes a “maximalist” position, “then we can’t get anything done … I do not see a path to a deal if they don’t budge, period.”

The clock is ticking, and no one is budging.