With time growing short before an Aug. 2 deadline to raise the federal debt limit, Republican and Democratic lawmakers meeting with Mr. Biden behind closed doors are just beginning to weigh the big fiscal trade-offs necessary for a compromise that could clear the way for a Congressional vote.

An accelerated schedule of meetings for next week will test whether the six members of the House and Senate talking with the White House are willing to entertain the serious political concessions and to make the hard choices needed to cut a deal in time.

In the colorful phrasing of Mr. Biden, the moment has arrived to find out who is willing to trade their side’s bicycle for the other side’s golf clubs.

“The really tough stuff that is left are the big-ticket items,” Mr. Biden said Thursday at the conclusion of the week’s third bargaining session, meetings that took lawmakers and administration officials to every corner of the federal budget in a search for consensus on ways to save federal dollars.

Lawmakers and aides say the negotiators quickly gobbled up low-hanging fruit like trimming agriculture subsidies and selling more of the telecommunications spectrum to generate revenue. There is a general consensus that federal workers are going to have to contribute more to their pensions, though the details are still to be determined. The Pension Benefit Guaranty Corporation will collect higher fees from stable companies, and some idle federal property could be up for sale.

But those actions are not going to produce anywhere near the $2 trillion or more in savings that both sides agree is the level required to win a debt limit increase while putting the government on course to save $4 trillion over the next decade — a goal set by Mr. Biden.

To get there, negotiators are going to have to make some excruciating choices about federal health care and safety-net programs, as well as the tax structure. At the same time, they need to reach a deal that not only can be sold to a bipartisan majority in the House and Senate, but also is credible enough to assure investors worldwide that Washington is getting serious about taking care of its financial health.

Representative Chris Van Hollen of Maryland, the senior Democrat on the Budget Committee and a participant in the talks, said one reason for setting three-hour meetings four times next week is to gauge whether he and his fellow budget bargainers can ever come to terms.

“We are picking up the pace in a big way, recognizing that we’ve got to determine whether we can reach agreement in principle or recognize that we are not able to bridge our differences,” he said.

Watching the clock, Senator Harry Reid, the Nevada Democrat and majority leader, on Friday called on the negotiators to keep working through the Fourth of July recess if necessary.

To Democrats, a major impediment is the Republican position against relying on any significant new revenues as part of the deal, insisting that most of the $2 trillion or more come from cuts in federal spending — although not from Pentagon spending, a major potential source of savings.

Democrats say they will never be able to sell a compromise without some new revenue to their colleagues in the House and Senate. They say the most affluent Americans should contribute to the debt limit deal through new taxes on hedge fund operators or by phasing out tax deductions for those at the highest levels of earnings.

But Representative Eric Cantor of Virginia, the majority leader who is representing House Republicans in the talks, on Thursday reiterated the deep Republican opposition to higher taxes.

“Our side will not support any attempt to raise the debt ceiling that is not accompanied by the kinds of cuts necessary or reforms necessary,” he said. “Nor will we support an attempt to raise the debt limit that raises people’s taxes. That, we don’t want to do.”

Republicans want to see Democrats embrace more changes in Medicare and Medicaid, the federal health programs for older Americans and the poor.

Democrats have so far pushed for modest changes like allowing the government to negotiate prescription prices with drug companies and to require drug industry rebates for people eligible for both Medicare and Medicaid — a proposal that could potentially generate tens of billions of dollars. But Democrats will not support any major Medicare overhaul, saying they believe that they have the political high ground on the issue at the moment.

To get a deal, lawmakers on both sides are going to have to bend considerably and back unpopular positions. They are then going to have to sell the plan to their rank and file on the grounds that they need to avert the economic disarray that could result from a failure to raise the debt ceiling.

Both sides say that all those in the talks want to reach a compromise. “There is no principal in that room that doesn’t want to get agreement,” Mr. Biden said.

Yet that is no guarantee that the deal will be done.

“I’m confident,” said Representative James E. Clyburn of South Carolina, another top Democrat in the talks. “But I’ve been confident before and come up short.”

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