President Bush encouraged a Republican senator Tuesday to offer Social Security legislation that would not include the private investment accounts that were the centerpiece of the plan Bush has promoted all year.

Bush's nod to Utah Sen. Bob Bennett (search) comes as public polls show that most Americans do not support the president's handling of the Social Security issue. Congress has been deadlocked on it.

Bennett said that during a luncheon with other Republican senators at the White House, he told the president of his plans to introduce the bill as early as next week.

"He indicated that I should go forward and do that," Bennett said. "And I'm grateful to have him do that even though his own preference would be to have personal accounts included."

Since the beginning of his second term, Bush has been pushing to allow younger workers to create voluntary personal accounts funded out of their Social Security payroll taxes. Democrats accuse the White House of seeking to privatize the Depression-era program and have been unified in opposition to the idea.

"I've decided that the Democrats have made it clear that they will not back personal accounts," Bennett said outside the White House. "And in response to the president's position that let's try to get something done, I will be proposing a bill that does not include personal accounts."

Bennett said some Democrats have told him privately that they would support such a bill, but he is not sure how many will be on board publicly now that he's introducing the legislation. He said he is looking for Democrats to co-sponsor the bill, but didn't have any to announce Tuesday.

"We've had a lot of interest," he said. "We have a lot of hope that we can use this bill to break the logjam and move forward on Social Security. We'll find out in the weeks to come."

Bennett said when he told Bush of his plans, "He just said, `I like your bill.' Period."

Bush and other supporters of private investment accounts argue they are needed to modernize the program. Under current projections, Social Security will begin to pay out more in benefits than it receives in tax receipts in 2017, and the trust funds will be depleted in 2041. At that point, benefits would be cut to adjust for the reduction in available funds.

An Associated Press-Ipsos poll earlier this month found 37 percent of Americans support Bush's handling of Social Security, while 59 percent disapprove. Those numbers hadn't budged after more than four months of the president barnstorming the U.S. to sell his plan.