WASHINGTON (CNN) - Following a meeting with key advisers, President Bush promised Thursday he would not raise payroll taxes to help pay for overhauling Social Security.

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"We will not raise payroll taxes to solve this problem," Bush told reporters during an Oval Office meeting with Social Security experts.

"The problem is America is getting older and that there are fewer people to pay into the system to support a baby boomer generation which is about to retire," the president said.

He again reassured retired Americans and those about to retire that nothing would change with the system, which first began paying retired workers monthly in 1940.

But now, the program is facing "unfunded liabilities of about $11 trillion," the president added, noting he's suggested a new way to help shore up its funds.

"I think it's vital to consider allowing younger workers, on a voluntary basis, to set aside some of their own payroll tax in personal accounts as part of a comprehensive solution to dealing with the Social Security issue," Bush said.

Republican Sen. Lindsey Graham of South Carolina had recommended a payroll tax increase on upper-bracket workers to help finance the transition.

The president vowed Thursday not to boost payroll taxes to pay for Social Security reforms. But enacting reforms will still be challenging.

The White House said this week the transition costs might be borrowed, but Bush said he would not prejudge any solution and would work with members of Congress.

Bush did not directly address whether the nation can afford to borrow to deal with the costs of changing to a partially private account-based system, which experts have estimated at $1 trillion to $2 trillion over 10 years.

"I will not prejudge any solution," Bush said.

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The president and many members of Congress from both parties broadly agree on the need for reforms to help keep Social Security solvent.

But there's lots of disagreement on how swiftly to move and whether to let workers put some of their payroll taxes into private accounts. For a rundown on some of these and other issues, click here.

Three years ago, a presidential commission proposed allowing individuals to place up to 2 percent of their payroll taxes into private accounts. But the government would have to replace those taxes that would otherwise fund benefits.

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Workers must pay 12.4 percent of wages into Social Security, up to a certain income limits ($87,900 this year; $90,000 in 2005). If you're self-employed, you pay the whole amount. If you work for someone else, your employer kicks in half (6.2 percent), and the funds finance monthly Social Security retirement checks for current recipients.

The White House said Monday it would considering borrowing to help finance the transition to a partially privatized system.

But aside from that, the government could increase the retirement age, which is already rising gradually to 67 under previous legislation.