Lawmakers from both parties opened budget talks with the White House on Thursday with a tacit agreement to focus on areas where they might find common ground that could produce significant savings and to postpone consideration of divisive issues such as higher tax rates and a dramatic overhaul of Medicare.

Democratic and Republican negotiators plan to broadly scrutinize the budget — targeting spending, tax breaks and other areas where they could save money — as they work toward a deal to rein in the spiraling national debt and smooth passage of a bill to raise the legal limit on government borrowing.

Congressional leaders emerged from the talks sounding optimistic that they would reach an accord — reassuring financial markets that Congress would probably approve additional borrowing and prevent the U.S. government from defaulting on its debt.

The apparent harmony at Blair House contrasted sharply with the atmosphere on Capitol Hill, where GOP lawmakers were publicly split on whether to step back from their most far-reaching priorities, including a plan to privatize Medicare in 2022, as part of the negotiations.

Senior Republicans such as House Majority Leader Eric Cantor (Va.), Ways and Means Committee Chairman Dave Camp (Mich.) and Budget Committee Chairman Paul Ryan (Wis.), who authored the Medicare plan, all underscored Thursday that a deal with Democrats on Medicare is virtually impossible.

At a policy breakfast sponsored by the journal Health Affairs, Camp said that he would not draft legislation to turn Ryan’s Medicare proposal into law this year, citing Democratic opposition. Nor, Camp said, would he move forward with a GOP plan to repeal President Obama’s health-care law.

“Is the repeal dead? I don’t think the Senate is going to do it, so I guess yes,” Camp told reporters.

Such statements sparked a backlash among conservative Republicans, who said House leaders were ceding too much ground too early in what are expected to be lengthy budget negotiations with Democrats.

Less than three weeks after the House passed his 10-year plan to shave $4.4 trillion from expected deficits, in part by turning Medicare into a private voucher system for seniors, Ryan said he would accept a deal to raise the debt limit in exchange for spending controls and cuts.

“We are under no illusion that we’re going to get everything we’ve always wanted in this one bill, but let’s get a good down payment,” Ryan said after a speech Thursday morning before the American Council for Capital Formation.

About two hours later at a Capitol news conference, House Speaker John A. Boehner (R-Ohio) insisted that the Medicare proposal remained a priority in the negotiations. “Let me make this clear: When it comes to increasing the debt limit and the need to have reductions in spending, nothing is off the table except for raising taxes,” Boehner said.

Several people present at the talks stressed that neither side took anything off the bargaining table during the first in a series of meetings. Major changes to entitlement programs and the tax code, they said, remain a possibility.

Sen. Rob Portman (R-Ohio), a former director of the Office of Management and Budget, questioned any decision to give up bargaining chips so soon. “It’s not a wise strategy to be taking things off the table today before we’ve begun any discussion to find consensus,” he said to reporters.

The dispute has both substantive and political implications. Top Republicans appear to be managing expectations for the debt-ceiling talks to prepare their rank and file for a compromise that is likely to fall short of the GOP’s grandest goals. But that strategy could backfire if party conservatives — particularly the 87 House freshmen — come to view such a result as a failure to push hard enough for significant, if politically risky, reforms.

Rep. Tim Scott (R-S.C.), who represents the freshmen in leadership, said in an interview that his class would demand “substantial, material and tangible cuts or there will be no deal.”

“To kick the can down the road on Medicare for any period of time is a risky, risky proposition,” Scott added. “There’s no question that everything else is dancing on the sidelines.”

With the nation’s debt poised to hit the limit of $14.3 trillion within the next two weeks, Cantor underscored the urgency of reaching a deal. “I think all of us understand we have got to achieve results,” he told reporters after the Blair House meeting.

“We are looking to find commonality, and so without attacking anyone’s plan we’re looking to find places we can agree,” said Cantor, who is representing House Republicans in the talks.

The Blair House talks, hosted by Vice President Biden, were initiated by Obama last month as part of his plan for far-reaching deficit reduction. The group will meet again Tuesday. In addition to Cantor, participants include Senate Minority Whip Jon Kyl (R-Ariz.), Senate Finance Committee Chairman Max Baucus (D-Mont.), Senate Appropriations Committee Chairman Daniel K. Inouye (D-Hawaii), Rep. James E. Clyburn (D-S.C.) and Rep. Chris Van Hollen (Md.), the senior Democrat on the House Budget Committee.

Treasury Secretary Timothy F. Geithner opened the talks with a sobering discussion of the economic impact of failure to achieve an accord to rein in borrowing and the importance of proving to the world that the United States can solve its budget problems, according to people present. Officials then went through details of the president’s deficit-reduction plan and the House budget.

The two sides agreed to begin trying to identify areas of overlap, though they did not discuss specific targets for a deal. This week Cantor offered a list of candidates, including cutting subsidies for wealthy farm operations and limiting lawsuits against doctors. Democrats said they could also foresee a compromise that includes cuts to defense spending.

Participants also said it may be possible to squeeze savings out of health-care programs or ending tax breaks for certain special interests without engaging in a full-on debate over tax and entitlement policy.

Staff writers Paul Kane and Felicia Sonmez contributed to this report.