The White House and Bennett both say they remain committed to private accounts, but the public has not embraced the proposal, and Democrats have refused to even negotiate unless the privatization plan is scrapped.

Fearing a stalemate, Bennett is seeking to unhitch the private accounts from his plan to keep the system from going broke by slowing the growth of future payments.

By separating the two elements, Bennett hopes to keep momentum for reform from withering and engage Democrats in discussions on how to keep the system solvent.

Bush supports that strategy and encouraged Bennett to proceed, the senator said Tuesday after a luncheon for Republican senators at the White House.

White House spokesman Taylor Gross said the president welcomes any ideas for strengthening Social Security.

"Nothing has changed in terms of his belief that voluntary personal accounts are an important part of any solution," Gross said.

In a statement, Senate Minority Leader Harry Reid, D-Nev., said Democrats will hold firm in their opposition unless Republicans abandon private accounts entirely.

"Until the president and the Republican leadership agree that their misguided attempt to privatize Social Security is over and they will no longer pursue their previously announced bait-and-switch strategy, Democrats will continue to refuse to enter negotiations over Social Security," he said.

The Democrats' concern is that the Senate could pass a bill without private accounts, but they could be added by House and Senate negotiators later, limiting Democrats ability to stop them.

"I came to the conclusion that if we didn't at least have an opportunity . . . for them to sign onto a bill that addresses the solvency problem, the whole thing would probably die, and I don't want it to die," Bennett said in an interview on CNN.

Bennett plans to introduce two pieces of legislation, possibly by the end of the week. One would establish private accounts and the other would seek to curb the growth in Social Security payments.

Under the Bennett solvency plan, the wealthiest Americans would have their payments tied to the growth in inflation, rather than current practice of tying them to the more rapid growth in wages. That would mean less money being paid out in future years, which some argue would be a benefit cut.

Those below the top tier would have their future payments determined by a growth index blending the inflation rate and wage increases. The poorest third of the population would continue to have their benefits grow based on the growth in wages, meaning there would be no change to the existing projections.

Bennett's plan is similar to one proposed by economist Robert Pozen.

David Certner, director of federal affairs for AARP, the leading organization representing people over 50, said the plan would hit the middle class too hard.

"It starts with the right idea of trying to insulate those at the bottom," he said.

"But the benefit cuts as you get into the middle class are steep, and they're steeper still as you get to people making 60, 70,000 a year."

It would also make Social Security "more of a welfare-type program" because those who pay the most into the system would no longer see that reflected in what they get out, Certner said.

The change is needed because the Social Security system is projected to begin paying out more than it takes in by 2019, and the Social Security Trust Fund would be out of money by 2052, according to the Congressional Budget Office.

The Social Security Trustees are even more dire in their projections, putting the years at 2017 and 2041, respectively.

Bennett said that he thinks if he can get one Democratic co-sponsor, others would follow.