GRAY COURT, S.C. — Republican presidential candidate Rick Perry proposed dramatic tax and spending changes Tuesday, saying he would let Americans choose between a 20 percent flat tax and the current system, allow private Social Security accounts and slash government spending and regulation.

Perry, seeking to regain the momentum he enjoyed in late August, said his plan would significantly spur economic growth. But analysts from the left and right said he would need draconian federal budget cuts to avoid massive deficits.

In a pitch to conservatives, the Texas governor said his “Cut, Balance and Grow” plan was bolder than what his Republican rivals or President Barack Obama would do. His proposal calls for gradually increasing eligibility ages for Social Security and Medicare and for amending the Constitution to require balanced budgets.

“America is under a crushing burden of debt, and the president simply offers larger deficits and the politics of class division,” Perry said.

After weeks of calling Social Security a “Ponzi scheme,” Perry proposed major changes to the program’s funding and payouts. Benefits would not change for current and soon-to-be retirees. Eventually, however, the eligibility age would rise, and wealthier people would see reduced benefits.

Younger workers could steer some of their Social Security payroll taxes to private investment accounts, an idea President George W. Bush tried and failed to enact in 2005.

The heart of Perry’s plan would reduce or eliminate an array of taxes. He would end taxes on Social Security benefits, estates, dividends and capital gains, which would most help upper-income people. He would lower the corporate income tax rate as well as the personal income tax rate for those who choose his 20 percent flat rate.

The top marginal tax rate on individual income is now 35 percent. It was 70 percent in the 1970s.

By design, Perry’s plan “must lose revenue” for the government, said Kevin Hassett, director of economic policy studies at the right-of-center American Enterprise Institute. To avoid higher deficits, Hassett said, the government would have to slash spending in ways not seen since after World War II.

Perry said his proposed deep cuts in tax rates and regulation would spur economic growth and thus generate significant new tax revenues. Economists have long debated the validity of such claims.

If Americans were allowed to choose between the current system and a 20 percent flat tax, several analysts said, the wealthy would get a big tax cut, and lower-income people would hardly be affected.

Perry acknowledged that many of his proposals are controversial. “I am not naive. I know this idea will be attacked,” he said.