NEW YORK -- As George W. Bush outlines his second-term plans tonight, one theme will be some unfinished business from his convention speech four years ago. Social Security, he said then, is called the third rail of politics, something you can't touch without getting a shock. "But if you don't touch it," he added, "you cannot fix it. And I intend to fix it."

He hasn't yet. But tonight, aides say, Mr. Bush will make the drive to put Social Security on sounder financial footing a centerpiece of his second-term agenda. In the process, he'll renew a call for a far-reaching change in one of the nation's most popular social programs: offering private accounts alongside the government benefits.

The project faces huge hurdles with enormous consequences for American politics and society. Mr. Bush's speech tonight isn't likely to get into the troublesome details that a credible fix for Social Security's long-term finances probably requires: some mix of retirement-age shifts, payroll-tax increases, benefit-level changes or further government borrowing.

Meanwhile, gone are the budget surpluses that might have paid the huge cost -- up to $2 trillion -- of a transition to a system that permits private accounts. And this cost clashes with an even-higher Bush priority, making his tax cuts permanent. Finally, the rocky stock market after the Internet bubble burst took away some of the allure of private accounts, which would probably be invested in stocks.

Adding private accounts to the mix not only wouldn't help fix the finances but would even add to the system's financial burden, at least at first. That's because a portion of payroll taxes would have to be diverted to the private accounts. But the government would remain obliged to pay full benefits for the millions already retired.

Mr. Bush appears determined to plow ahead, both to rescue and to overhaul the social-insurance plan. The politics of Social Security are so treacherous that some advisers urged Mr. Bush to stay away. Any kind of tinkering invites charges of imperiling a sacred program, one benefiting not only retirees but also the disabled and some others. In Congress, some moderate Democrats inclined to work with Mr. Bush have been burned by the partisanship of his first term.

The finance issue is pressing. As the number of retirees grows, fewer workers are having to support each one by their payroll taxes. Starting about 2019, payroll taxes won't be enough to pay promised benefits, according to current projections. The leading edge of a demographic tsunami will hit at the end of the next presidential term, as the first baby boomers reach age 62 and some claim early-retirement benefits. "If we delay," Federal Reserve Chairman Alan Greenspan said last week, "the adjustments could be abrupt and painful."

Mr. Bush's aides hope a Social Security call to action, with limited details, can help him with a key part of the electorate without igniting a firestorm. The idea of personal investment accounts alongside Social Security, say campaign advisers, plays well with younger voters who doubt that Social Security will be there for them when they're old. This age group includes many of the voters most soured on the president over Iraq.

Advisers also say the focus will set Mr. Bush apart from Democratic nominee John Kerry, who has been mostly mum about the looming funding crisis.

Veterans of past Social Security wars suggest what a Bush overhaul might look like: Younger workers would be allowed, but not required, to have private accounts in addition to getting federal benefits. Of payroll taxes -- currently 12.4% deducted from the first $87,900 of wages -- perhaps two percentage points could be diverted to fund private accounts. Workers who wanted an account could invest this money in mutual funds sanctioned by the government.

But if the accounts are to help buttress Social Security overall, a tough issue has to be decided. Proponents of the accounts expect that workers generally will come out ahead on retirement with their combination of some Social Security benefits plus returns on their investment accounts. The question is, by how much can the government reduce their benefits, to reflect in some measure the higher earnings they've gotten in the market, and thus reduce Social Securities' liabilities?

Some aides felt Mr. Bush should skip this nest of controversy. Economic adviser Stephen Friedman and Chairman Gregory Mankiw of the Council of Economic Advisers, among others, argued that he had a good first-term record and should run on achievements, notably tax cuts, with a promise to protect them. This was even though the aides themselves believe in Social Security reform.

Overpowering the stay-the-course faction was an influential big-idea camp. It argued that Mr. Bush needed a compelling domestic agenda, in part to offset the predominant focus on the war in Iraq. In this group were political advisers Karl Rove and Ken Mehlman, Treasury Secretary John Snow and budget director Josh Bolten.

The next question was what big idea -- Social Security reform, tax reform or both? No particular tax reform option ever took hold. The conclusion: Mr. Bush could campaign on a vague call to restructure and simplify the tax code, and leave details to later and to Congress.

When the topic turned to Social Security, the debate among Bush advisers was over how the president would answer dicey questions about details. Mr. Rove, among others, argued that he could avoid specifics, as he did in 2000 and has so far in this campaign.

Mr. Bush was talking about Social Security this week. "We want people owning their own retirement accounts," the 58-year-old president told a crowd in Taylor, Mich., on Monday. "Listen, baby boomers like me are just fine when it comes to Social Security. But for you younger workers out there, look carefully ... at the fiscal solvency of the Social Security system. I believe younger workers ought to have the option of taking some of their own money and putting it in personal savings accounts that they can call their own."

The upshot of the debate among advisers, some aides say, is that the president tonight will propose both tax reform and a Social Security overhaul, including a private-account option. That will give him an opening to claim a mandate for either, or both, if he's re-elected
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The double approach leaves one advocate of private accounts, Sen. John Sununu of New Hampshire, skeptical. "I don't think it's realistic to expect to be able to accomplish both in a single presidential term," says Mr. Sununu, son of a chief of staff for Mr. Bush's father.

He is among just a few congressional Republicans urging President Bush to focus on the issue. House Speaker Dennis Hastert, who is pushing a tax-overhaul plan of his own, has urged the president to leave Social Security on the shelf. Republicans, though they expect to retain their narrow House majority this year, will soon turn to worrying about 2006. The prospect of a Social Security battle scares them.

In his first term, Mr. Bush never proposed Social Security legislation and largely ignored the divided recommendations of a Social Security Commission he had named. In December 2001 it offered three options for an overhaul that would include private accounts. Two called for adjustments in benefit levels, while the third would have had the government finance the transition cost with borrowing.

As for what a reform proposal in a second Bush administration might look like, some clues can be found in advisers' behind-the-scenes infighting in 2001.

Internal documents that former Treasury Secretary Paul O'Neill gave author Ron Suskind for his book "The Price of Loyalty" suggest this: a plan to let younger workers open personal accounts by diverting 4% of wages (but $1,000 a year maximum) that otherwise would go toward the Social Security payroll tax. The accounts would be voluntary. Benefits for current retirees and people 55 and older would be unaffected.

In discussing the issue, Bush officials never settled on the hard part: how to finance the private accounts without making the system's finances even weaker -- given the diversion of that 4%. If workers divert some of their payroll taxes to private accounts, revenue to pay their grandparents' benefits must come from somewhere. Diverting just two percentage points of payroll taxes would create a gap of up to $2 trillion over the first 10 years, according to various projections.

Former economic adviser Lawrence Lindsey favored making up this gap with additional federal borrowing. Treasury officials and Mr. Bush's Council of Economic Advisers were opposed. Since the president had ruled out tax boosts, the only alternative, these officials argued, was to curb the growth of benefits. Treasury officials looked to Mr. Bush for guidance.

An internal Treasury memo dated Oct. 25, 2001, on approaching the president is instructive as to some of the hard choices. Prepared by staffers for Secretary O'Neill, it said Mr. Bush needed to be asked, "Is he willing to live with benefit cuts (i.e. 'pain'). ... What is the meaning of 'voluntary' (does he want to inflict pain on everyone, or just those who voluntarily opt out of the system?)" It's unclear whether Mr. Bush ever was asked these questions or gave answers. The Social Security issue was soon shelved for the rest of his term.

A document the Treasury Department prepared for Mr. Bush at the time stated, "Even with the higher returns from personal accounts, there are only two ways to make the program fiscally sustainable" -- increase revenues or "slow the rate of benefit growth."

Some who favor partial privatization of Social Security are urging the administration to back the approach of Peter Ferrara at the conservative Institute for Policy Innovation. It calls for creating larger private accounts and covering the transition cost by having the Treasury borrow the money. This plan is the basis of a reform bill from Sen. Sununu and Republican Rep. Paul Ryan of Wisconsin.

Backers of the plan boast that Social Security's chief actuary attests that this approach wouldn't require either benefit cuts or tax increases. But, as the liberal Center on Budget and Policy Priorities notes, the actuary also said that over 75 years (the time frame often used to assess the Social Security program's solvency), the plan would require taking $68 trillion from general federal revenue.

The administration rules out higher payroll taxes to improve solvency or to add a private-account option. To cure the solvency problem, that leaves benefit changes, which could take various forms -- none politically popular.

Both Mr. Bush and Mr. Kerry rule out raising retirement ages to reflect today's longer life spans. The age for collecting full benefits already has risen beyond 65 for current workers, depending on when they were born, and is set to gradually rise to 67 by 2027.

A major cost-saver would be to index workers' future benefits to inflation. Currently they're indexed to the increase in wages, which usually rise faster than the cost of living.

"Means testing" -- with wealthy seniors forfeiting some amount of their benefits -- could also help the finances. The highest-earning elderly already pay income taxes on some of their benefits. While Democrats traditionally have been averse to means-testing benefits, Mr. Kerry recently argued that he and his wealthy wife, Teresa Heinz Kerry, shouldn't expect to collect all the benefits they're due.

If private accounts were part of an overhaul, another option would be to trim the benefits of those future retirees whose personal accounts end up producing high investment earnings.

While aides suggest that Mr. Bush, in a second term, would keep to his practice of leaving the legislative details to Congress, some Republicans say the president will have to drop that approach if he wants to be taken seriously and achieve his goal. And, many in Congress add, he might have to agree to some tax increases to get the job done.

"The president has to not only talk in terms of the concept but to lay out a detailed plan," says Sen. Lindsey Graham, a proponent of partial Social Security privatization. The South Carolina Republican says he would support raising the amount of wages that are subject to payroll taxes and closing unspecified corporate tax loopholes.

Democratic Sen. John Breaux of Louisiana, who gave up his hope of cutting a Social Security deal with Mr. Bush and is now retiring, says a re-elected Mr. Bush would have to "leave all options on the table, including his tax cuts for upper-income taxpayers."

Such talk won't make it any easier for Mr. Bush to persuade wary Republicans to play along. Most Republicans, Sen. Graham says, "are scared as hell. It's enough to make me discouraged."