WASHINGTON -- Republican Sen. Lindsey Graham of South Carolina startled the capital's conservative network last month with a speech on Social Security reform at the Heritage Foundation. His call for private accounts was sound conservative doctrine, but he proposed financing it with a huge payroll tax increase for upper bracket Americans. This was heresy, conservatives said, by Strom Thurmond's successor.

 Graham responds this is the only way President Bush's priority reforms will be passed. He states two axioms his fellow conservatives will not address. First, Social Security -- the government's most popular program -- cannot be saved without "some sacrifice." Second, the personal accounts Republicans want cannot be passed without bipartisan cooperation -- meaning a high-profile Democratic co-sponsor.

 Thus, Graham is proposing a bargain of historic proportions. To reform Social Security, each party must do something unthinkable. Democrats would have to swallow personal accounts declared anathema by the AARP, organized labor and every sector of the party. Republicans would have to go along with a tax increase falling heavily on the party's base.

 Graham is a 49-year-old country trial lawyer just finishing his second year as a senator, but lack of seniority has not bothered him previously. Elected to Congress in the Republican sweep of 1994, he helped lead the coup that almost ousted Newt Gingrich as speaker of the House in 1997 and in fact fatally wounded him. Ever since his 2002 election to the Senate, he has been pressing Social Security reform, and he now has the ear of important White House aides.

 On Nov. 18, Graham introduced a bill that looks, superficially, like other Republican proposals. Current Social Security beneficiaries and workers aged 55 and older would not be affected. Workers aged 54 and younger could set aside 4 percentage points of their 12.4 percent Social Security payroll tax for private accounts that they and their heirs would keep forever. The distinctive Graham twist is that workers "who don't want to take part in a modernized system" would be taxed at higher rates -- rising over the years.

 Graham's bill and accompanying statement did not address the elephant in the living room that Republicans ignore: an estimated $1 trillion in transition costs. He did address it, however, in his Heritage speech. Ruling out financing the cost through federal borrowing, his answer is the un-Republican solution of higher taxes -- raising the $87,900 income limit subject to the payroll tax by an unspecified amount. Boosting it to $200,000 will completely pay for transitional costs in 10 years. As revenues grow, Graham's plan would reduce the 12.4 percent payroll tax rate.

 This is a net tax hike for upper-middle income taxpayers who voted for George W. Bush as a tax cutter, not a tax hiker. Such an outcome would be hard for Republicans to swallow, and early reaction has been negative. "I just think Lindsey is trying to be virtuous," one supply-side theorist told me. Graham responded: "Virtuous? I'm just trying to be practical."

 His tax plan, Graham believes, is the only way he can attract Democratic co-sponsors for private accounts. Democrats correctly have viewed millions of lower income Americans holding stock and bond funds as a dagger at their breast. The voter who has discovered the joys of financial markets is automatically a potential Republican convert.

 Although Democrats may find it even harder to accept private accounts than for Republicans to accept a higher tax base, there are Senate Democrats who qualify as possible co-sponsors: old-fashioned fiscal conservatives from "red" states who might buy into Graham's bargain. Ben Nelson of Nebraska and Bill Nelson of Florida are obvious, but both are junior senators. Graham needs a senior Democrat who has pounded away at the Bush deficits, such as Max Baucus or Kent Conrad, ranking Democrats on the Finance and Budget committees respectively.

 It is difficult to measure the accumulated conventional wisdom on both sides of the aisle Graham must overcome. Time is not on his side. With Social Security heading the president's second-term agenda, he feels he has no more than six months to sell his plan. His bargain would be painful for both sides, but nobody else has an idea with a chance to succeed.