Senior Republicans conceded Wednesday that a deal is unlikely on a contentious plan to overhaul Medicare and offered to open budget talks with the White House by focusing on areas where both parties can agree, such as cutting farm subsidies.

On the eve of debt-reduction talks led by Vice President Biden, House Majority Leader Eric Cantor (Va.) said Republicans remain convinced that reining in federal retirement programs is the key to stabilizing the nation’s finances over the long term. But he said Republicans recognize they may need to look elsewhere to achieve consensus after President Obama “excoriated us” for a proposal to privatize Medicare.

That search could start, Cantor said, with a list of GOP proposals that would save $715 billion over the next decade by ending payments to wealthy farmers, limiting lawsuits against doctors, and expanding government auctions of broadcast spectrum to telecommunications companies, among other items.

Democrats said they were encouraged by the move, which could smooth the way to a compromise allowing Congress to raise the legal limit on government borrowing and avoid a national default.

“There’s common ground there,” said Rep. Chris Van Hollen (Md.), the senior Democrat on the House Budget Committee, who is representing House Democrats in the Biden talks.

The conciliatory tone signals the opening of a new and more consequential phase in the battle to design an affordable government for an aging society. After months of partisan brinkmanship over comparatively small cuts to the current budget, lawmakers returned to Washington this week to confront the harder problem of reducing a national debt that has risen to alarming levels.

They face a tight deadline: Without congressional action, the debt will hit the legal limit of $14.3 trillion in the next two weeks. Treasury Secretary Timothy F. Geithner has said he can juggle the books and pay the bills through Aug. 2. But at that point, the U.S. government would risk a default on its obligations and economic disaster.

Congressional leaders in both parties, eager to avoid that outcome, are dispatching representatives to the Biden talks to try to hash out a debt-reduction accord that would make it easier for lawmakers to cast a politically difficult vote for additional borrowing.

Even the more austere spending plan drafted by House Budget Committee Chairman Paul Ryan (R-Wis.) and approved last month by the House would require an increase in the debt ceiling of about $1.9 trillion to cover the government’s bills through September 2012.

With voters growing increasingly anxious about the debt, Republicans and some Democrats are refusing to approve additional borrowing without an explicit strategy to reduce deficit spending. Raising the debt limit will be particularly difficult in the House, where the Republican majority is dominated by conservatives who have vowed to oppose any additional borrowing.

In the Biden talks, Cantor said, he would press for all the provisions in the Ryan proposal, including changes to Medicare and Medicaid that would produce hundreds of billions of dollars in savings and dramatically transform both programs. He challenged Obama to provide specifics of his own deficit-reduction plan, which calls for modest changes to the programs. But with Democrats showing no inclination to engage seriously on entitlements, Cantor said, the Ryan budget offers many other avenues for compromise.

Cantor added that House Republicans want an agreement that includes three elements: spending cuts in the 2012 budget, which covers the fiscal year that begins Oct. 1; enforceable targets that would require Congress to continue racheting down spending in future years; and action by the end of this year on legislation that would begin to meet those targets.

“We don’t want to rely solely on caps and targets. We want to take action now,” Cantor said, noting that budget controls have too often been waived when lawmakers have found them difficult to meet.

The immediate action, Cantor said, should involve cuts to mandatory programs, which make up the largest portion of the budget and are not funded through annual appropriations. For such programs, the government is obliged to provide benefits to all who qualify regardless of the cost.

The biggest mandatory programs — often called “entitlements” — are Medicare, Medicaid and Social Security. But Cantor said negotiators could avoid the “big three,” which Democrats have vowed to defend, by focusing on changes in other areas. “If we can come to some agreement [and] act to effect those savings now, this year, it will yield a lot of savings in subsequent years,” he said.

At a breakfast for reporters hosted by Bloomberg News, Ryan echoed that view, saying, “We’re not going to get a grand-slam agreement . . . because of just the political parameters” set by Obama. But Ryan said his budget offers a “menu of options . . . that I think we could get that are not necessarily the global agreement on, say, Medicare or Social Security.” That menu includes proposals from Obama’s budget request, such as ending grants for worsted-wool producers and requiring graduate students to pay interest on college loans while they are still in school.

Other options would be less palatable to Democrats. Ryan has proposed slashing $127 billion from the food-stamp program, which was expanded during the recent recession. He has also suggested cutting contributions to federal worker pension plans and eliminating the new Consumer Financial Protection Bureau, a centerpiece of recent legislation overhauling financial regulations.

Still, the offer suggests that Republicans and Democrats are engaging in the same exercise, scouring the proliferation of debt-reduction plans in hopes of cobbling together enough mutually acceptable ideas to cut a deal.

As talks progress, Van Hollen said Democrats will insist on scrutinizing the tax code just as thoroughly. One fat target for savings, he said, is tax breaks for major oil producers. “We still want the overall approach to be a balanced one” that does not focus just on spending cuts, he said.

Cantor dismissed tax hikes as a “non-starter,” saying raising taxes without changes to the big entitlement programs would simply delay the day of reckoning.

“We want to be there with a safety net for people who need it. But what we’ve seen over the years is a country that has turned much more into an entitlement country for people who don’t need it,” Cantor said. “That is the fundamental question at stake here.”