The prospect of further cuts worries health care providers because it comes on top of the new health care law, which reduced payments to most providers to help offset the cost of extending coverage to millions of uninsured Americans.

While Mr. Obama has signaled a willingness to make health spending a top source of budget savings in the current debate, he has not sent a similar message on Social Security, even though in budget talks with Republicans this year he entertained the idea of changing the way annual increases in payments are calculated. The president did not mention changes to Social Security in his latest speech, a fact that could bolster Democrats who believe they may have a new political opening on that program, given that Gov. Rick Perry of Texas, a top Republican presidential candidate, has attacked the program as a government-sponsored Ponzi scheme.

But Mr. Obama has said that “health care cuts” need to be part of any deal, and he has already given a preview of the cuts he is likely to propose next week. In April, he unveiled a framework for deficit reduction that he said would save $480 billion in Medicare and Medicaid by 2023.

In negotiations with Congressional Republicans in July, Mr. Obama went further. He indicated that he was willing to consider a gradual increase in the age of eligibility for Medicare and cuts in federal payments to states for Medicaid.

Medicare and Medicaid account for 23 percent of federal spending this year, and their costs are growing faster than the rest of the budget because of increasing enrollment and medical inflation. Under current law, the Congressional Budget Office says, the two programs will account for 28 percent of federal spending in 2021.

Controlling these costs is a goal for Republicans on the powerful House-Senate committee on deficit reduction, whose proposals are supposed to receive up-or-down votes in both chambers before the end of the year.