The White House yesterday further explained President Bush's Social Security proposal, detailing how contributions to new personal investment accounts would be offset by dollar-for-dollar reductions in Social Security's guaranteed benefits.

Even as new details emerged, however, Bush's plan stirred fresh political worries among Republicans and brought calls from some legislators to abandon the idea of personal accounts.

Retirees now are guaranteed a monthly check, based largely on years worked and payroll taxes paid into the system. Under Bush's plan, workers could invest some of their payroll taxes in stocks and bonds, accumulating savings and investment returns in personal accounts that would be theirs upon retirement. In exchange, workers would accept a smaller monthly check from the Social Security Administration.

Specifically, workers who opt for the accounts would lose a proportionate share of their guaranteed Social Security payment, plus interest equal to the amount that money would have earned if the government had invested it in Treasury bonds. Those lost benefits would be recouped if workers' investments realized a return equal to or greater than the 3 percent earned by Treasury bonds now held by the system.

It is still not clear how Bush's retooled system would work in total. The White House has chosen to discuss only the private accounts. But they will not close the projected $3.7 trillion gap between benefits promised over the next 75 years and taxes expected to be collected. That gap would have to be closed through yet-to-be-detailed benefit cuts.

Here is how Bush's personal-account system would work:

If a worker set aside $1,000 a year for 43 years, and earned 4.6 percent annually on investments, the account would grow to $221,552 in today's dollars. That money probably would be paid out upon retirement in increments of $15,952 a year, according to calculations by the Center for Budget and Policy Priorities, a liberal advocacy group. A White House calculation showed a smaller payout.

But guaranteed benefits would be reduced by approximately $151,990 — the amount the worker contributed to his personal account, plus 3 percent interest above inflation. The remainder, $69,562, would be the increase in benefits the worker would receive over his lifetime above the level he would have received if he stayed in the traditional system. That sum as an annual payout would total $5,008.

But that benefit gain could be substantially smaller. The Congressional Budget Office, Capitol Hill's official scorekeeper, factors out stock-market risks to assume a 3.3 percent rate of return and then subtracts 0.3 percent for expected administrative costs on the account. Under that scenario, the full amount in a worker's account would be reduced dollar for dollar from his Social Security checks, for a net gain of zero.

If investments earned less than 3 percent a year above inflation, a worker would do worse than in the traditional system.

Meanwhile, in an unexpected blow to the administration, Rep. Jim McCrery, R-La., chairman of the subcommittee that handles Social Security, said Bush should scrap the idea of financing the accounts with money earmarked for the Social Security trust fund.

"It seems to me that if we insist on diverting payroll tax revenue," McCrery said, "we have ensured opposition from the AARP and probably every single Democrat in the House and Senate, and that's not a good place to start."

Two House Republicans with years of expertise on Social Security offered an alternate plan: Bolster the current program with money from general revenues.

"I think politically it's the most salable. It's not going to scare anybody," said Florida Rep. Clay Shaw, former chairman of the House Ways and Means subcommittee on Social Security. "It does preserve Social Security as it is today. If we're going to attract some Democrats, that's the way to go."

Bush, for his part, took his campaign on the road.

In Fargo, N.D., the president stressed his willingness to work with Congress, saying, "All options are on the table except for running up payroll taxes."

Later, in Great Falls, Mont., he was trying to sway Sen. Max Baucus, ranking Democrat on the Senate Finance Committee that has jurisdiction over Social Security. Before Bush's arrival, Baucus held a town-hall meeting and said the majority of the several hundred people present opposed Bush's plan.

"They're against it because it undermines Social Security as they know it," Baucus said. "They're afraid of the plan. They're afraid of private accounts."

Bush will continue to press his case today in Omaha, Neb., Little Rock, Ark., and Tampa, Fla., and Tuesday in Detroit.

McCrery's comments were reported by the Los Angeles Times.