In his 2010 "Road Map for America's Future," the Wisconsin congressman proposed a plan to allow younger workers to divert more than one-third of their Social Security taxes into personal accounts that they would own and could will to their heirs.
Ryan wrote that the accounts would provide workers an opportunity "to build a significant nest egg for retirement that far exceeds what the current program can provide." Workers 55 and older would stay in the current system.
Romney hasn't embraced the proposal and Ryan, chairman of the House Budget Committee, didn't include it in either of the federal budgets passed by House Republicans the past two years. But now that Ryan is running for vice president, Democrats hope to capitalize on the issue.
Bush's proposal for private accounts received a chilly reception from members in both parties in Congress, though Ryan embraced it. Democrats used the issue against GOP congressional candidates in the 2006 election, when they regained control of the House and Senate.
"The very last thing we ought to be doing is putting at risk the retirement security of millions of America's seniors," said Rep. Debbie Wasserman Schultz of Florida, who heads the Democratic National Committee.
Until now, Social Security had been largely absent from the presidential campaign. President Barack Obama has yet to lay out a detailed plan for addressing the issue, and his silence is drawing criticism from advocates who supported him in the past. Romney has been more forthcoming with proposals, but Social Security has not been a big part of his campaign, either.
Romney, in his book, "No Apology," said he liked the idea of personal accounts. But, he wrote, "Given the volatility of investment values that we have just experienced, I would prefer that individual accounts were added to Social Security, not diverted from it, and that they were voluntary."
Romney's current plan for Social Security doesn't mention personal accounts. Instead, he proposes a gradual increase in the retirement age to account for growing life expectancy. For future generations, Romney would slow the growth of benefits "for those with higher incomes."
Romney says tax increases should be off the table, and current beneficiaries and those near retirement should be spared from cuts.
"Mitt Romney and Paul support gradual reforms to Social Security that protect current beneficiaries from any benefit disruptions while strengthening the program to ensure that it doesn't go bankrupt," Romney campaign spokesman Ryan Williams said.
The trustees who oversee Social Security say the trust funds that support the program will run dry in 2033. At that point, Social Security will generate only enough tax revenue to pay about 75 percent of benefits, triggering automatic cuts unless Congress acts.
During the 2008 campaign, Obama said he wanted to improve Social Security's finances by applying the payroll tax to annual wages above $250,000. It is now limited to wages below $110,100, a level that increases with inflation.
Obama also pledged to oppose raising the retirement age or reducing annual cost-of-living adjustments, or COLAs. "Let me be clear, I will not do either," Obama said at the time.
Last year, however, Obama put on the table a proposal to reduce annual COLAs during deficit-reduction talks with House Speaker John Boehner, R-Ohio. The talks ultimately failed and nothing came of the proposal, but it raised questions about whether Obama would honor his 2008 pledge.
"A national politician would do well to strongly identify themselves with Social Security, not just with rhetoric, but to be very clear that they understand the pain people are experiencing today, that they stand behind this program and they will protect the citizenry and they will not cut benefits," said Eric Kingson, a Syracuse University professor who co-founded Social Security Works. "I hope to hear that from the White House. I have not heard that yet."
Obama offered some principles to strengthen Social Security in his 2011 State of the Union address.
"We must do it without putting at risk current retirees, the most vulnerable or people with disabilities, without slashing benefits for future generations and without subjecting Americans' guaranteed retirement income to the whims of the stock market," Obama said in the speech.
Last week, Vice President Joe Biden made a more sweeping guarantee during a campaign swing in southern Virginia, telling a customer at a diner that Social Security will not be changed.
"I guarantee you, flat guarantee you, there will be no changes in Social Security," Biden told the customer, according to a White House pool report. "I flat guarantee you."
A Biden adviser said later the vice president was merely reassuring the woman that her benefits would not be changed. The adviser spoke on condition of anonymity because he was not authorized to speak publicly about the issue.
Obama campaign spokesman Adam Fetcher said the president "has put forward a set of principles to guide bipartisan action to strengthen it for future generations. Rather than laying the groundwork for a bipartisan approach as the president has done, Mitt Romney's only solution would mean deep benefit cuts for future retirees. His running mate, Paul Ryan was an architect of privatization."
Romney's campaign chided Obama's inaction.
"His failure to lead on entitlements has put the future of Social Security at risk," said Williams, the Romney spokesman. "Mitt Romney is committed to ensuring that Social Security is there for future generations and he has a comprehensive plan to save Social Security with commonsense reforms."