WASHINGTON — The dueling deficit-cutting plans presented by congressional Republicans and President Barack Obama promise to restore the nation’s fiscal credibility. But if they fail to deliver, the result could be still higher deficits and the potential for another devastating economic crisis.

Even if the far-reaching and painful measures like those in the two proposals were adopted, economists say, more drastic action would be required in the years ahead to bring the deficit down to a sustainable level.

The GOP plan, drafted by Rep. Paul D. Ryan of Wisconsin, would reduce government red ink by $4.4 trillion over 10 years. It would cut federal spending by $5.8 trillion, but would offset that by $4.2 trillion in tax cuts. Ryan counts on the tax cuts to stimulate the economy and end up delivering substantially more tax revenues.

Obama would shrink deficits by $4 trillion over 12 years. He would make considerably smaller spending reductions, a total of $2 trillion, but would increase taxes by about $1 trillion, focusing on wealthy Americans. Since his definition of wealthy begins with families earning $250,000 a year, many working couples with hefty salaries but few if any tax shelters could feel the effects of his plan more sharply than the millionaires and billionaires he often talks about.

Obama’s savings rely in good part on future efforts by government regulators to hold down the costs of medical care — a major, but yet untested, element in the health care law that does not take full effect until 2014.

The Ryan-Republican plan and the one outlined by Obama in his speech last week are opening bids in what’s expected to be a drawn-out battle along partisan lines. But the two approaches agree on one thing: Over time, the nation’s mounting debt threatens the economic stability of the whole country, and the government — along with most voters — will almost certainly have to find ways to do more with less.

“Everybody’s sacred cows are going to be gored” if meaningful deficit reduction is to be achieved, said Augustine Faucher, an economist who specializes in government budgets for Moody’s Analytics.

Without a credible plan to reduce the deficits, the U.S. could face the kind of debt crisis that has engulfed Greece, Spain and Portugal — with global investors demanding sharply higher interest payments on American debt, driving up borrowing costs for the U.S. and its citizens, and hence hurting domestic investments, job growth and the nation’s standard of living.

“When I look out at the horizon, what worries me the most is that the deficits come crashing down and shatter confidence” in the international markets, said Jim Kessler, vice president for policy at Third Way, a moderate Democratic think tank. His other big concern: “The budget will be so dominated by entitlements (such as Medicare) that we won’t be able to help our economy grow” with funds for such things as education and research.

A central element of Ryan’s plan is to end Medicare’s historically open-ended commitment to cover the medical bills of the elderly. Seniors would be given a set amount of money to buy private insurance and would be expected to make up the difference out of their own pockets.

The vouchers Ryan calls for would almost certainly be smaller than the premiums on the private insurance seniors would be expected to buy, unless health care costs declined sharply instead of soaring as they have been. The elderly would have to make up the difference.

According to an analysis by the nonpartisan Congressional Budget Office, seniors would need to pay about $6,400 more in 2022 than under the existing system. Economists estimate that based on current income measures, no more than a fifth of Americans 65 and older could afford such additional financial burdens.

Ryan’s plan would also cap federal spending on Medicaid, which helps the poor and disabled but also pays the nursing home and other long-term care bills for millions of seniors who have no substantial financial means of their own. Absent the federal payments, some or all that cost could be shifted to families of the elderly.

Another key element in the Ryan plan is the idea that maintaining the George W. Bush-era tax rates for the wealthy and lowering the top individual and corporate tax rates — to 25 percent from the current 35 percent — would generate hefty investment and economic gains that would sharply bolster government revenues and help to reduce the deficit.

Economists say that idea was tested during the early 1980s under President Ronald Reagan and in the last decade under President George W. Bush — and in each case failed to deliver the promised economic growth or tax revenues.

“We tried really big experiments, and neither time did we get the results we expected,” said Dean Baker, co-director of the left-leaning Center for Economic and Policy Research.

Macroeconomic Advisers, a leading economic forecasting business, examined the Ryan tax plan and his projection that big cuts in federal services would generate almost immediate payoffs to the economy in the form of lower interest rates and stronger economic and employment growth. “We consider the analysis both flawed and contrived,” the company concluded.

On the Democratic side, Obama’s plan to raise $1 trillion in additional tax revenues includes generating $320 billion by limiting itemized deductions for the wealthiest 2 percent of taxpayers. This would be in addition to letting the Bush-era tax cuts expire at the end of 2012 for individuals making $200,000 or more.

Republicans, who control the House, have ruled out higher taxes in any form.

Even if Obama prevailed, many economists believe the deficit could not be brought down to manageable levels in the longer term without raising taxes on some middle-class taxpayers as well as the rich. In fact, Obama endorsed overhauling the nation’s complicated tax code, which would most likely raise the prospect of eliminating such deep-rooted provisions as mortgage interest deductions — hitting a wider spectrum of people than just the very wealthiest Americans.

“I’m sympathetic to the president’s wish to focus on tax increases on the very high incomes, but that’s not going to be enough,” said Alan Auerbach, a University of California, Berkeley professor and former deputy chief of staff for Congress’ Joint Committee on Taxation. “We’ll eventually need more revenue than those tax increases will generate to solve the long-run budget problems we face.”

While Ryan’s plan relies heavily on the magic of trickle-down economics, Obama is betting on the promise of “bending the cost curve” in health care through a series of administrative measures that may or may not work. Rather than overhauling Medicare, Obama proposes to save hundreds of billions in federal health care spending, for example, by using the government’s purchasing leverage to drive down prescription drug costs. (Such bargaining is now prohibited by law.)

Obama’s plans to shave $770 billion in nonsecurity discretionary spending and $400 billion in the defense budget are also fraught with economic and political risks.

Government spending, including Obama’s stimulus programs, have pumped needed cash into the economic recovery, and the president’s speech makes it clear there won’t be any new stimulus measures to support growth.

“We should be focusing on the 8.8 percent unemployment (rate)” said economist Baker, expressing concerns about the fragile recovery.

At the same time, many of Obama’s spending cuts are certain to encounter stiff resistance from Republicans and industry as well as from unions and local communities dependent on federal contracts for jobs.

Just two months ago, the Pentagon’s latest five-year budget had incorporated about $400 billion of reductions, partly through administrative efficiencies. Now the president is calling for an additional similar amount over the next decade, which experts say would probably mean shrinking the size of the military or scrapping some major weapons systems.

“We’ve already cut the low-hanging fruit,” said Todd Harrison, a senior fellow at the Center for Strategic and Budgetary Assessments. “It certainly will have an impact on the defense industry,” he said, and that will spill over into the broader economy.

But given the contrasting and combative position Obama has staked out — he said there’s “nothing serious or courageous” about Ryan’s plan and insisted there won’t be tax cuts for the wealthy — the president’s biggest challenge may be his ability to break the political impasse.

Failure to do so could have dire consequences for his political future — and, more important, for the economy.

William Howell, a public policy professor at the University of Chicago, sees compelling reasons for Obama and the Republicans to come to an agreement. Obama doesn’t want to leave a legacy as a president who presided over a profligate government that could affect generations to come, he said, while the GOP leadership will need to deliver on a issue that ranks as most crucial for many insurgent “tea party” activists.

On the other hand, Howell is far less confident when he considers the past record and current political realities. “I think the most likely outcome is we see modest to meek changes in the immediate future, with promises of greater changes down the road,” he said.