Obama administration officials are offering to cut tens of billions of dollars from Medicare and Medicaid in negotiations to reduce the federal budget deficit, but the depth of the cuts depends on whether Republicans are willing to accept any increases in tax revenues.

Administration officials and Republican negotiators say the money can be taken from health care providers like hospitals and nursing homes without directly imposing new costs on needy beneficiaries or radically restructuring either program.

Before the talks led by Vice President Joseph R. Biden Jr. broke off 12 days ago, negotiators said, they had reached substantial agreement on many cuts in the growth of Medicare, which provides care to people 65 and older, and Medicaid, which covers lower-income people. Those proposals are still on the table when Congress reconvenes this week, aides said, and are serious options that Democrats could accept in exchange for Republican concessions that raise revenues.

“Congress smells blood,” said William L. Minnix Jr., the chief lobbyist for nonprofit nursing homes.

Mr. Minnix, the president of a trade group known as LeadingAge, is urging nursing homes to “bombard your senators with the message that Medicaid cannot be cut by $100 billion” over 10 years, as President Obama and many Republican lawmakers have suggested.

A coalition of hospital lobbyists, worried about the direction of the budget talks, has begun a national advertising campaign to block further cuts in the two health care programs, which account for about 55 percent of hospital revenues. The hospitals have made a commitment to spend up to $1 million a week through August on television, print and online advertising.

“This is white-knuckle time for a lot of people,” said Bryant Hall, a health care lobbyist whose clients include drug and biotechnology companies. “Stakeholders and beneficiaries are anxiously watching the budget negotiations.”

They may have reason to be anxious.

Senator Charles E. Schumer of New York, the No. 3 Senate Democrat, said: “We are very willing to entertain savings in Medicare. Medicare gives very good health care very inefficiently.”

In return, Mr. Schumer said, Republicans should be willing to consider some additional revenue.

Negotiators said they were seriously considering cuts in Medicare payments to hospitals for uncollectible patient debt and the training of doctors; steps to eliminate Medicare “overpayments” to nursing homes; a reduction in the federal share of some Medicaid spending; and new restrictions on states’ ability to finance Medicaid by imposing taxes on hospitals and other health care providers.

Medicare and Medicaid insure more than 100 million people, account for 23 percent of all federal spending and are likely to be an important part of any budget deal. Military spending, which accounts for about 20 percent of federal expenditures, is likely to be included as well.

READ MORE: MSNBC