Despite growing concerns about the country’s long-term fiscal problems and an intensifying debate in Washington about how to deal with them, Americans strongly oppose some of the major remedies under consideration, according to a new Washington Post-ABC News poll.

The survey finds that Americans prefer to keep Medicare just the way it is. Most also oppose cuts in Medicaid and the defense budget. More than half say they are against small, across-the-board tax increases combined with modest reductions in Medicare and Social Security benefits. Only President Obama’s call to raise tax rates on the wealthiest Americans enjoys solid support.

On Monday, Standard & Poor’s, for the first time, shifted its outlook on U.S. creditworthiness to “negative” because of the nation’s accumulating debt. The announcement rattled investors and could increase pressure on both sides in Washington to work out a broader deal as part of the upcoming vote over increasing the government’s borrowing authority.

The president and congressional Republicans have set out sharply differing blueprints to deal with the looming problem. Obama has called for agreement on at least a framework by early summer, which roughly coincides with the deadline for raising the nation’s debt ceiling.

Public resistance to many proposals in the competing plans could greatly complicate those discussions. Altering entitlement programs still involves political risk, the poll shows, and proponents of such changes face a substantial challenge in persuading the public that they are needed.

The two sides are far apart philosophically, and neither enjoys great public confidence: Fifty-eight percent of those polled disapprove of the way the president is handling the budget deficit. Even more — 64 percent — give Republicans in Congress low marks.

The public is split about evenly on whether Obama or congressional Republicans are more trusted to find the right balance between cutting unnecessary spending and preserving priorities.

On that question, public opinion is unchanged since last month, despite the recent battle over funding the government for the rest of the current fiscal year, resulting in a deal that includes $38 billion in cuts and that came barely an hour before the government was scheduled to shut down.

Congressional Republicans maintain a narrow edge over Obama when it comes to taking a “stronger leadership role” in Washington, 45 to 40 percent. And political independents side with the Republicans on tackling the burgeoning debt. But Obama maintains a key, double-digit advantage among independents when it comes to “protecting the middle class.”

The Republican budget plan, drafted by House Budget Committee Chairman Paul Ryan (Wis.) and approved by the House last week, calls for a major restructuring of Medicare and Medicaid, with sizable savings in future costs. Obama, in his plan, opposes the GOP’s restructuring, but he has said that future savings will be needed to keep Medicare solvent.

The Post-ABC poll finds that 78 percent oppose cutting spending on Medicare as a way to chip away at the debt. On Medicaid — the government insurance program for the poor — 69 percent disapprove of cuts.

There is also broad opposition to cuts in military spending to reduce the debt, but at somewhat lower levels (56 percent).

In his speech last week, the president renewed his call to raise tax rates on family income over $250,000, and he appears to hold the high ground politically, according to the poll. At this point, 72 percent support raising taxes along those lines, with 54 percent strongly backing this approach. The proposal enjoys the support of majorities of Democrats (91 percent), independents (68 percent) and Republicans (54 percent). Only among people with annual incomes greater than $100,000 does less than a majority “strongly support” such tax increases.

An across-the-board tax increase is decidedly less popular, at least when coupled with benefit reductions. A report by the National Commission on Fiscal Responsibility , co-chaired by former senator Alan Simpson (R-Wyo.) and former Clinton White House chief of staff Erskine Bowles, recommended “shared sacrifice.” But in the poll, a slim majority — 53 percent — opposes small tax increases and minor benefit cuts for all as a way to significantly reduce the debt. Strong opposition to that kind of solution outnumbers strong support by 2 to 1.

There is broad support for keeping Medicare structured the way it has been since it was instituted in 1965: as a defined-benefit health insurance program. Just 34 percent of Americans say Medicare should be changed along the lines outlined in the Ryan budget proposal, shifting it away from a defined-benefit plan. Under that proposal, recipients would select from a group of insurance plans providing guaranteed coverage, and the government would provide a payment to the insurer, subsidizing the cost. Advocates say this approach is more sophisticated than a pure voucher plan.

In his speech last week, Obama attacked that idea, saying it could leave some Americans without adequate coverage and would end “Medicare as we know it.”

While the debt issue lingers, most Americans — 59 percent — do approve of the deal stitched together to avoid a government shutdown by cutting billions from this year’s budget.

The telephone poll was conducted April 14 to 17 among a random national sample of 1,001 adults. The margin of sampling error is plus or minus 3.5 percentage points.

Polling manager Peyton M. Craighill contributed to this report.