President Clinton and congressional leaders agreed last night that the government should safeguard Social Security's future and provide some form of Medicare prescription drug coverage. But in a White House meeting, they differed on details -- and remained especially far apart on the key question of how deeply to cut taxes amid the nation's booming economy.

As Congress reconvened yesterday with tax cuts and spending bills at the top of its agenda, the president invited its top party leaders to talk in broad terms about how to divide up anticipated budget surpluses of as much as $1 trillion outside of Social Security over the next decade.

Although the administration preceded the hour-long meeting with sharp criticisms of GOP proposals for deep tax cuts, both sides emerged fairly upbeat. Republican leaders, in particular, emphasized areas of general agreement, such as using a "lock-box" mechanism to earmark Social Security surpluses to extend the program's solvency for several years.

"The president is pretty much committed to locking away those Social Security dollars to preserve Social Security and Medicare for the future," House Speaker J. Dennis Hastert (R-Ill.) said after the meeting. He said lawmakers and the president also tentatively agreed to provide some sort of prescription drug coverage for Medicare recipients, although Republicans contend that Clinton's plan for universal coverage is unnecessary and too costly.

"There's an opportunity in this Congress that we can do some really big things, some tremendous things," Hastert said in an interview.

The gathering raised the curtain on mid-summer negotiations that will determine the level of tax cuts as well as spending on major programs under circumstances that Congress and the White House haven't seen in decades: the looming end of budget deficits and the beginning of sizable surpluses. Some private groups, however, warned yesterday that the surpluses may be smaller than the government has projected.

Clinton has called for about $250 billion in targeted tax cuts over 10 years. Republicans want more than three times that amount. The White House proposal, which many congressional Democrats embrace, reflects the belief that most Americans place a higher priority on safeguarding popular social programs than on getting a tax break in today's strong economy.

Republican House and Senate leaders, however, are pressing for significant tax relief across the board. The House Ways and Means Committee will begin work today on an $864 billion tax cut over 10 years, and the Senate Finance Committee will follow suit next week with its own $792 billion plan. GOP leaders said future spending cuts will make the tax cuts affordable without damaging important government programs.

Even as he prepared to greet the congressional leaders, Clinton dispatched his top budget advisers to attack GOP tax cut proposals that they said would jeopardize Social Security, Medicare, military spending and major domestic programs in the future.

The nation is still thriving, Treasury Secretary Lawrence Summers told reporters, "and that is what is put at risk by the dangerous reversal of course that would be represented by huge tax cuts."

Gene Sperling, who oversees White House economic policy, said that "it's puzzling, disturbing and disappointing that the Republicans now put forward a tax cut plan that leaves zero -- zero -- for Medicare over a 10-year period."

Some Republicans excluded from the meeting fired back. They said there's ample room for significant tax cuts in light of White House estimates of an overall $5.9 trillion surplus over the next 15 years.

"The only reason for this surplus is because taxpayers are paying too much, which is why they deserve a refund," Rep. Bill Archer (R-Tex.), chairman of the Ways and Means Committee, said in a statement. "If we don't cut taxes now and the money stays in Washington, the politicians surely will spend it."

Archer calls for phasing in a 10 percent across-the-board tax cut, reducing capital gains taxes, eliminating the "marriage penalty" couples pay for filing taxes jointly and phasing out the estate and gift taxes inheritors pay. In the Senate, Finance Committee Chairman William V. Roth Jr. (R-Del.) has proposed a $792 billion tax cut targeted more at middle-class Americans.

Along with smaller tax cuts, Clinton's budget plan would pour billions more into Medicare and devote about $127 billion more to military spending and about $200 billion more for other domestic programs.

The liberal-leaning Center on Budget and Policy Priorities said yesterday that the surplus forecasts are premised on the improbable notion that the government will indefinitely remain within the austere and "politically unrealistic" spending caps imposed by the 1997 balanced-budget deal. If those caps are lifted, more than half of the projected surplus would vanish, the center's study said.

The think tank added that the surplus forecasts by the Congressional Budget Office and the White House budget office do not anticipate future emergency spending for natural disasters or war, and they overstate the likely reduction in interest payments on the national debt. The study concludes that the non-Social Security surplus that Congress is counting on for tax cuts may well total no more than $127 billion over the coming decade.

Robert D. Reischauer, a former CBO director and a budget expert with the Brookings Institution, said it was reckless for tax-cut advocates to be "acting as if we have money in the bank when really all we have is a promissory note."

But tax-cut advocates say that regardless of shortcomings in the projections, those are the numbers Congress must use.

"By low-balling it, these critics can pull the rug out from under Republican tax-cutters," said Stephen Moore of the libertarian Cato Institute.

Staff writer Juliet Eilperin contributed to this report.

CAPTION: GOP leaders speak to media after meeting with the president. From left are Senate Majority Leader Trent Lott, House Majority Leader Richard K. Armey and Speaker J. Dennis Hastert.