GRAY COURT, S.C. — Gov. Rick Perry of Texas unveiled a plan on Tuesday to scrap the graduated income tax and replace it with a 20 percent flat rate. By throwing out rates as high as 35 percent and eliminating estate and investment taxes, the plan would grant a major tax cut for the wealthy. It is the centerpiece of an ambitious proposal that aims to overhaul political sacred cows like Social Security and Medicare while slashing the federal budget.

Mr. Perry, a Republican presidential candidate, said his proposal would also offer benefits to middle-class Americans by giving a $12,500 deduction for every member of a household while preserving exemptions for state and local taxes, mortgage interest and charitable contributions for anyone making less than $500,000. He said anyone could still file under the current code, and he also pledged to lower the corporate tax rate to 20 percent, from 35 percent.

“Taxes will be cut on all income groups in America,” said Mr. Perry, who promised that taxes could be filed on a postcard-size form under his plan. “The net benefit will be more money in Americans’ pockets, with greater investment in the private economy instead of the federal government.”

The plan represents a gamble for Mr. Perry, who is trying to reinvigorate a once-high-flying campaign by capturing some of the energy Herman Cain generated with his flat tax plan and by drawing a sharply conservative contrast with Mitt Romney.