WASHINGTON - They're not buying it. Most Americans say they don't believe Medicare has to be cut to balance the federal budget, and ditto for Social Security, a new poll shows.

The Associated Press-GfK poll suggests that arguments for overhauling the massive benefit programs to pare government debt have failed to sway the public. The debate is unlikely to be resolved before next year's elections for president and Congress.

Americans worry about the future of the retirement safety net, the poll found, and 3 out of 5 say the two programs are vital to their basic financial security as they age. That helps explain why the Republican Medicare privatization plan flopped, and why President Barack Obama's Medicare cuts to finance his health care law contributed to Democrats losing control of the House in last year's elections.

Medicare seems to be turning into the new third rail of politics.

"I'm pretty confident Medicare will be there, because there would be a rebellion among voters," said Nicholas Read, 67, a retired teacher who lives near Buffalo, N.Y. "Republicans only got a hint of that this year. They got burned. They touched the hot stove."

Combined, Social Security and Medicare account for about a third of government spending, a share that will only grow. Economic experts say the cost of retirement programs for an aging society is the most serious budget problem facing the nation. The trustees who oversee Social Security and Medicare recently warned the programs are "not sustainable" over the long run under current financing.

Nearly every solution for Social Security is politically toxic, because the choices involve cutting benefits or raising taxes. Medicare is even harder to fix because the cost of modern medicine is going up faster than the overall cost of living, outpacing economic growth as well as tax revenues.

"Medicare is an incredibly complex area," said former Sen. Judd Gregg, R-N.H., who used to chair the Budget Committee. "It's a matrix that is almost incomprehensible. Unlike Social Security, which has four or five moving parts, Medicare has hundreds of thousands. There is no single approach to Medicare, whereas with Social Security everyone knows where the problem is."

That's not what the public sees, however.

"It's more a matter of bungling, and lack of oversight, and waste and fraud, and padding of the bureaucracy," said Carolyn Rodgers, who lives near Memphis, Tenn., and is still working as a legal assistant at 74. "There is no reason why even Medicare, if it had been handled right, couldn't have been solvent."

In the poll, 54 percent said it's possible to balance the budget without cutting spending for Medicare, and 59 percent said the same about Social Security.

Taking both programs together, 48 percent said the government could balance the budget without cutting either one. Democrats and political independents were far more likely than Republicans to say that neither program will have to be cut.

The recession cost millions their jobs and sent retirement savings accounts into a nosedive. It may also have underscored the value of government programs. Social Security kept sending monthly benefits to 55 million recipients, like clockwork; Medicare went on paying for everything from wheelchairs to heart operations.

Overall, 70 percent in the poll said Social Security is "extremely" or "very" important to their financial security in retirement, and 72 percent said so for Medicare. Sixty-two percent said that both programs are extremely or very important.

The sentiment was a lot stronger among the elderly. Eighty-four percent of those 65 or older said both programs are central to their financial security. Compare that to adults under 30, just starting out. Just under half, or 46 percent, said they believed both Social Security and Medicare would be extremely or very important to their financial security in retirement.

Old, middle-aged or just entering the workforce, most people are keenly aware of the cost of health care, and that may be helping to focus more attention on Medicare.

"Health insurance these days is very costly, and it's not something that most people can afford to go out and buy on their own," said Tim Messner, 38, a technology quality assurance analyst from Barberton, Ohio. "I don't know that we could possibly plan ahead for medical insurance, but if you had to replace Social Security or investments, you at least have an idea of what you can live on."

Numbers tell the story. As health care goes up, the value of Medicare benefits is catching up to Social Security's. A two-earner couple with average wages retiring in 1980 would have expected to receive health care worth $132,000 through Medicare over their remaining lifetimes, and $446,000, or about three times more, in Social Security payments.

For a similar couple who retired last year, the Medicare benefit will be worth $343,000, compared to Social Security payments totaling $539,000, less than twice as much. The numbers, from economists at the nonpartisan Urban Institute, are adjusted for inflation to allow direct comparison. For low-income single retirees and some couples, the value of expected Medicare benefits already exceeds that of Social Security.

The poll found a deep current of pessimism about the future of Social Security and Medicare. As much as Americans say the programs are indispensable, only 35 percent say it's extremely or very likely that Social Security will be there to pay benefits through their entire retirement. For Medicare, it was 36 percent.

Again, there's a sharp difference between what the public believes and what experts say. Most experts say the programs will be there for generations to come. But they may look very different than they do today, and Americans should take note.

"Do they have a basis for worrying that these programs are going to pay them much less than they're currently promising?" asked economist Charles Blahous. "Yes, absolutely. Do they have a basis for being concerned that the programs may have to be structurally changed in order to survive? The answer to that is yes, too." A trustee of Social Security and Medicare, Blahous served as an economic adviser to President George W. Bush.

Republican lawmakers don't inspire much confidence right now when it comes to dealing with retirement programs, the poll found. Democrats have the advantage as the party more trusted to do a better job handling Social Security by 52 percent to 34 percent, and Medicare by 54 percent to 33 percent. Often, but not always, major revisions have been accomplished through bipartisan compromise.

Sue DeSantis, 61, a store clerk from West Milton, Ohio, worries she won't be able to rely on either program. Both are important to her well-being, but she thinks changes are inevitable. And she has little confidence in lawmakers.

"I don't put my faith in politicians, and I don't put my faith in the government," said DeSantis. "I'm a Christian. I believe that God will take care of me. That doesn't mean I should be foolish and not look at anything, but I don't believe that the politicians are necessarily going to do the best for the common ordinary person like myself."

The Associated Press-GfK poll was conducted May 5-9, 2011, by GfK Roper Public Affairs & Corporate Communications. It involved landline and cell phone interviews with 1,001 adults nationwide and has a margin of sampling error of plus or minus 4.2 percentage points.

Associated Press Polling Director Trevor Tompson, Deputy Director Jennifer Agiesta and AP News Survey Specialist Dennis Junius contributed to this report.

Online: Poll results: http://www.ap-gfkpoll.com