Republicans opened their drive in the Senate for a $792 billion tax cut yesterday by beating back a much smaller Democratic plan, but they were forced to accept a 10-year limit on their tax package.

Democrats seized on an obscure budget rule to force the Republicans to limit their tax cut plan to the coming decade. Because the GOP plan is heavily backloaded -- with many of its most important features not to take effect fully until later years -- yesterday's action could frustrate Republican efforts to return a large portion of future surpluses to taxpayers in the form of tax cuts.

Nonetheless, Senate Majority Leader Trent Lott (R-Miss.) declared it a "happy day" for Republicans as they moved toward passage of a GOP plan that would provide broad-based income tax relief, eliminate the so-called marriage tax penalty, and offer numerous breaks to defray educational and health care costs and reduce the estate tax.

"Each of the measures . . . is vitally important to the well-being of all families," said Senate Finance Committee Chairman William V. Roth Jr. (R-Del.), the chief author of the plan. "Our purpose is to be broad-based -- to provide the most meaningful tax relief possible."

But even as the Senate began its opening arguments on the floor, Federal Reserve Chairman Alan Greenspan reiterated his misgivings about a tax cut at this time, saying he would prefer that the anticipated budget surpluses be used to retire the federal debt.

"We probably would be better off holding off on a tax cut immediately, largely because it is apparent that the surpluses are doing a great deal of good to the economy," Greenspan told the Senate Banking Committee.

At the same time, the Clinton administration issued a statment "strongly" opposing the Republican tax cut and reiterating that the president would veto it. The White House argues that the GOP plan is too big and would threaten efforts to shore up Medicare and other domestic spending programs.

The House passed a comparably sized -- but differently structured -- package of tax cuts last week, and Senate leaders are pushing for a final vote on their plan by Friday. House and Senate GOP leaders hope to have a compromise bill worked out before Congress adjourns at the end of next week. But they have indicated that they may not send the bill to the White House until September, to deny Clinton the opportunity to have a big midsummer veto ceremony while they're back home during the congressional recess.

As the Senate began considering alternative tax cut proposals yesterday, it rejected a $290 billion Democratic plan that targeted relief to middle- and lower-income families by increasing the standard deduction and also providing a variety of education, child care and other tax credits.

While both Republicans and Democrats favor setting aside two-thirds of the $3 trillion in projected surpluses over the coming decade to shore up Social Security's finances, Democratic leaders said that their more modest tax plan would also leave substantial resources for Medicare reform and other critical domestic spending.

But the Democratic plan went down, 60 to 39, with all Republicans voting no and six Democrats also voting against it -- Sens. Evan Bayh (Ind.), Robert C. Byrd (W.Va.), John Edwards (N.C.)., Joseph I. Lieberman (Conn.), Robert G. Torricelli (N.J.) and Paul D. Wellstone (Minn.). Some of these Democrats oppose any tax cut.

Arguing that Congress should wait to see if the projected surplus is real before reducing taxes, Lieberman and Carl M. Levin (D-Mich.) said they will offer an amendment to strike out the entire tax cut.

Greenspan, whose public pronouncements carry enormous weight in fiscal debates, seem ingly offered similar advice during his appearance yesterday. He suggested that a tax cut at this point would cut into future surpluses and risk "a great deal of positive good to the economy."

The Fed chairman told the Banking Committee that it would be unwise to cut taxes now on the basis of surplus forecasts that could be far off the mark.

If Congress goes ahead with a major tax cut, "I think it also has to be prepared to cut spending significantly in the event that the forecasts on which they are based are proved wrong," he said.

Another reason for waiting, the Fed chairman said, is that sooner or later the economy is going to slow down, "and having the availability of significant tax cuts at that point, in my judgment, will be very useful."

"I am by no means against cutting taxes," he continued, but it would be much better for the economy to reduce the debt owed to the public. The surpluses already achieved have lowered long-term interest rates, encouraged more business investment and begun to increase the government's ability to borrow in the future, he said.

The fate of the tax cut probably won't be determined until later this fall, when the White House and congressional leaders attempt to negotiate a final deal on spending, taxes, Medicare and Social Security. Some moderate Republicans and fiscal conservative Democrats say that there is a deal to be struck over a $500 billion tax cut roughly half way between what the GOP leadership is demanding and what the White House has proposed.

Sen. John Breaux (D-La.), a chief author of the moderates' plan, warned that "we are heading for a financial train wreck" this fall unless the two sides seek common ground. But Senate Minority Leader Thomas A. Daschle (D-S.D.) cast doubt over the prospects of an eventual split-the-difference compromise, saying he saw "absolutely no room . . . zero chance" for a tax cut of more than $300 billion.

Lott and the Republicans were forced to limit their tax plan to 10 years after running afoul of a budget rule barring tax legislation that results in revenue losses after the tenth year. The $792 billion GOP tax plan would cost an additional $2 trillion or more in the subsequent 10 years, according to some estimates. The Republicans sought to waive the rule but encountered stiff resistance from Democrats, losing on a largely party-line vote of 51 to 48.

The 10-year provision would weaken the impact of the bill and also could complicate the long-term investment strategies of individuals and businesses.

But GOP leaders tried to put a positive face on their setback, saying the legislation could still be extended in coming years and that Americans would still enjoy substantial benefits. Moreover, they said, by limiting the plan to 10 years, the Republicans can counter one of the Democrats' strongest criticisms, that the tax cut would "explode" in cost early in the next century.

"It's a crummy way to do tax policy, but I'm sure we'll be able to change it in 18 months," after the election, said Senate Majority Whip Don Nickles (R-Okla.). "The practical effect for the time being is it will be temporary."

Staff writer John M. Berry contributed to this report.