Talks to avert a potentially catastrophic debt default resume on Tuesday after signs Republicans might soften their stance over a main obstacle to a deal with Democrats, but hopes for a breakthrough remain slim.

Vice President Joe Biden leads senior lawmakers in their third round of negotiations to lift the $14.3 trillion U.S. debt limit before an August 2 deadline for action.

A congressional aide said the session would focus on savings in Medicare and Medicaid, government-funded healthcare at the core of so-called federal entitlement programs that have emerged as a major block to an agreement.

Top Republicans say Biden’s talks are laying vital groundwork for an eventual compromise on measures to pare down the U.S. budget deficit, but President Barack Obama will ultimately be required to seal the deal.

No one expects anything to happen fast, but attention has shifted to Biden’s group after separate discussions among a group of six senators stalled last week. It will meet in Senate offices on Capitol Hill at 3 p.m..

Failure to increase the debt limit could force the United States to renege on its debt obligations, risking devastating fallout for the country and world economies.

“We face a lot of real problems. We shouldn’t manufacture problems,” said White House budget chief Jacob Lew. “The debt limit is going to have to be extended. That’s a political, not an economic crisis. We have an economic problem. We could turn it into a crisis by failing to act,” he told CNBC television.

Republican leaders in the House of Representatives will stage a vote next week to raise the debt limit by $2.4 trillion, knowing the measure will fail because it will not be accompanied by spending cuts, aides said on Tuesday.

The vote will underscore support among their ranks for significant spending cuts and budget reforms, as opposed to the Obama administration’s desire for a “clean” bill to lift the borrowing limit without any strings attached.

Republicans say they are open to a compromise on their plan to slash healthcare costs to trim trillions of dollars from the U.S. budget deficit in return for raising the debt ceiling.

Democrats, led by Obama, say they too want to control spending, although they have criticized cuts proposed by Republicans as too drastic.

But Democrats also want to boost revenue by raising taxes, which Republicans flatly reject as part of a debt deal, a clear warning that financial markets should expect negotiations to push right up to the brink of default before a deal is done.

“I don’t think the most brilliant negotiators, with the best of intentions, can resolve this problem,” said Scott Lilly, a former congressional budget specialist and now a senior fellow with the Center for American Progress.

HEALTHCARE IN FOCUS

Republicans want deficit savings to match the amount the administration wants to raise the borrowing limit, and the U.S. Treasury sees a $2 trillion increase in the debt ceiling needed to last through the November 2012 elections.

Tackling healthcare could signal the group had moved beyond some of the areas where compromise was easier to reach to begin getting at politically tougher issues.

Analysts at the non-partisan Committee for a Responsible Federal Budget estimate that savings to the U.S. budget deficit of between $25 billion and $130 billion could be achieved over 10 years by increasing the costs to people in the Medicare program for the elderly.

Biden’s group has initially focused on areas where the two sides can most easily agree. These could yield deficit savings of between $1 trillion and $2 trillion over the next decade, according to the nonpartisan budget committee.

Biden’s group includes four Democrats and two Republicans, including Eric Cantor, the party’s No. 2 in the House.

Cantor said the group was only laying the groundwork for final talks among Obama, House Speaker John Boehner, the top Republican in Congress, and Senate leaders.

The United States reached the congressionally mandated $14.3 trillion limit on its borrowing on May 16. Officials are using special accounting measures to avoid a default for now.

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By Alister Bull and Richard Cowan

WASHINGTON