Speaking at the Americans for Prosperity Foundation’s annual meeting, Mr. Romney said his plan would cap spending at 20 percent of gross domestic product by 2016, and would require $500 billion a year in spending cuts. To accomplish this, Mr. Romney explained, he would eliminate all nonessential government programs, including Amtrak, return federal programs like Medicaid entirely to the states and improve the productivity and efficiency of the federal government. He would also immediately cut all nonsecurity discretionary spending by 5 percent across the board.

Mr. Romney’s proposal for Medicare is similar to the hotly debated plan that Representative Paul Ryan of Wisconsin, the chairman of the House Budget Committee, introduced in April. Mr. Ryan’s plan would replace Medicare and offer payments to older Americans to buy coverage from the private market.

Mr. Romney’s proposal would give beneficiaries the option of enrolling in private health care plans, using what he, like Mr. Ryan, called a “premium support system.” But unlike the Ryan plan, Mr. Romney’s would allow older people to keep traditional Medicare as an option. However, if the existing government program proved more expensive and charged higher premiums, the participants would be responsible for paying the difference.

He presented his plan as offering more choice — though younger Americans would need to be prepared to possibly pay more, for instance, depending on which plan they selected.
“Younger Americans today, when they turn 65, should have a choice between traditional Medicare and other private health care plans that provide at least the same level of benefits,” he said. “Competition will lower costs and increase the quality of health care.”

He concluded, “The future of Medicare should be marked by competition, by choice, and by innovation, rather than by bureaucracy, stagnation and bankruptcy.”
       
His plans for Social Security did not include any privatization plans, which some of his Republican presidential rivals support. Instead, “for the next generation of retirees, we should slowly raise the retirement age,” he said. “And finally for the next generation of retirees, we should slow the growth of benefits for those that have higher incomes.”

Americans for Prosperity was co-founded and financed by David H. Koch. Mr. Koch, a billionaire who, along with his brother, Charles, runs Koch Industries, sat at a table in the front row at the meeting. Mr. Romney received a lukewarm welcome, with only tepid applause throughout, rising for an ovation only when he promised to repeal “Obamacare,” the president’s health care legislation.
“I should have started with that line,” he said.

Mr. Romney previewed his speech at a town-hall-style forum Thursday evening in Exeter, N.H., and he also laid out the basics of his overall vision in an op-ed column in USA Today.

“Tomorrow’s Medicare should give beneficiaries a generous defined contribution and allow them to choose between private plans and traditional Medicare,” Mr. Romney wrote. “And lower-income future retirees should receive the most assistance. I believe that competition will improve Medicare and the coverage that seniors receive.”

Democrats wasted no time in attacking Mr. Romney’s plan, saying that not only would it effectively end Medicare and Medicaid, but also that his tax cuts would disproportionately benefit the wealthy.
“Romney apparently operates under the false assumption that we can just cut our way to prosperity,” James Kvaal, the policy director for Obama for America, said in an e-mail. “In recent months, he has embraced extreme ideological approaches like Representative Paul Ryan’s budget plan and the ‘cut, cap and balance’ proposal. He would return American families to the failed economic policies that contributed to the years of rising inequality, stagnant wages and eroding middle-class security.”
Republicans also criticized the plan, including Gov. Rick Perry of Texas, who said in a news release that Mr. Romney’s refusal to rule out future government bailouts put him at odds with true fiscal conservatives.

“While Mr. Romney continues to put Wall Street over Main Street, Rick Perry is a real fiscal conservative whose economic plan ends Washington and Wall Street bailouts, cuts taxes and federal spending and balances the budget by 2020,” said Ray Sullivan, a Perry spokesman, in an e-mail statement.

In his speech, Mr. Romney repeated what seems to be his new mantra — “making government simpler, smaller and smarter” — and cast the issue of spending cuts in moral terms.
“We cannot with moral conscious borrow trillions of dollars that can only be repaid by our children,” he said. “We cannot so weaken our economic foundation that we jeopardize our ability to preserve freedom.”

As he did Thursday night, he also contrasted his time running companies in the private sector with how Solyndra, a solar power company that received government funds and is now facing bankruptcy and scandal, was run.

“They had robots that whistled Disney songs, I’m not kidding,” Mr. Romney marveled. “They had what was described as spa-like showers, with liquid crystal displays that told you what temperature the water was.”
       
“When I get to the White House — hopefully — no one will need to teach me how to balance budgets,” he said. “I’ve been doing that for 35 years.”