House Republican leaders agreed yesterday to make their huge tax cut proposal conditional on progress in reducing the national debt, apparently averting a threatened revolt by GOP moderates as they prepared to try to pass the bill today.

The last-minute tweaking appeared to clear the way for passage of a 10-year, $792 billion tax reduction, the centerpiece of the GOP agenda. House Speaker J. Dennis Hastert had begged for Republican unity on the package, which would lower income tax rates for all Americans, slash capital gains taxes, phase out the estate tax entirely and reduce the "marriage penalty."

Moderates led by Rep. Michael N. Castle (R-Del.) had complained that the tax cut was just too big, arguing that it would use too much of projected surpluses and leave too little for key domestic programs and debt relief. But after a tense day of behind-the-scenes talks, Castle and Ways and Means Committee Chairman Bill Archer (R-Tex.) worked out language that will leave the $792 billion figure intact, while ensuring that a 10 percent across-the-board reduction in income tax rates will be phased in only if the interest on the national debt doesn't rise in any given year.

House GOP leaders previously agreed to scale back their original plan, from $864 billion to $792 billion, to placate the moderates and to skirt a budget rule that would have left the bill vulnerable to a challenge in the Senate.

But Hastert (R-Ill.) and other leaders refused to make any further concessions on the size of the tax cut, fearing that it would undermine their position in future negotiations with the White House. Last night, as the House began its debate key lawmakers on both sides of the aisle predicted the tax plan would pass. The House voted 219 to 208 to begin the debate, with Constance A. Morella (Md.) and Greg Ganske (Iowa) the only Republicans voting no. The final vote was put off until today because the talks took so long.

"We know how many horses there are in the herd," said Majority Leader Richard K. Armey (R-Tex.). "It's just a question of how to get them all in the barn."

President Clinton used his nationally televised news conference to once again denounce the Republican tax cut plan as a threat to continued economic prosperity and warned that it would soak up money needed to bolster Social Security and Medicare and reduce the nation's $5.5 trillion debt. Democrats also cited figures from a liberal think tank estimating that almost half the tax benefits in the GOP plan will go to Americans making more than $300,000 a year.

Everyone on Capitol Hill seems to favor some kind of tax cut, and the president's budget proposal calls for about $250 billion in tax cuts over 10 years. But Clinton insisted the Republican plan went too far and indicated he would veto such a package.

"We face a critical choice," Clinton said. "Whether to move forward with the fiscal discipline that got us to where we are today or return to the kind of risk-taking that got us into recessions and deficits before."

GOP moderates have a reputation for capitulation on Capitol Hill, and yesterday's deal is likely to revive that reputation. As late as yesterday afternoon, some moderates were saying there was no way they would support the $792 billion figure, but most appeared to be on board last night.

Rep. Charles B. Rangel (N.Y.), the ranking Democrat on Ways and Means, said that the concession to the moderates "does not reduce the debt we leave to our children by a single dollar," while others said it was bad tax policy that would add an element of uncertainty to the tax code. Rep. Barney Frank (D-Mass.) dismissed the compromise as a "wholly implausible scheme" concocted by the Republicans to avoid the humiliation of the tax bill going down.

If the bill does pass, it will be a sweet victory for Hastert, who has struggled to lead the House with a mere five-vote majority. In one-on-one meetings with recalcitrant Republicans, Hastert had made it clear he believed his credibility as a leader was riding on the success of the tax plan. According to one participant, Hastert declared, "I'm staking my speakership on this and I need your vote." Several other holdouts said he asked: What would it take for you to support this bill?

"There's obviously a lot of pressure in this situation," Castle said. "They keep saying how important this is to the party."

There are two schools of thought on the 40 or so Republican moderates, who meet for lunch every Tuesday but rarely manage to coordinate their strategies. In one view, they are the wimps of the House, invariably yielding to the conservative wing of the party on key legislation. In the other view, they are a quietly influential check on the far right of the GOP, subtly shifting the party toward the political center in a nonconfrontational way.

Rep. Sherwood L. Boehlert (R-N.Y.) subscribes to the hidden-power theory. If the moderates are such pushovers, he says, then why has the party's leadership never made good on its promises to eliminate the Department of Education and other Cabinet agencies? Why are House leaders hinting about a minimum wage increase this year?

"Anybody who thinks the moderates aren't shaping public policy just isn't paying attention," Boehlert said.

Still, most House moderates acknowledge that they are rarely a driving force behind GOP legislation and that they often end up voting for conservative bills they consider less than ideal. Most of them are from the Northeast, and many represent urban areas; their party's base is in the South and West, and in rural and suburban areas. They are a minority of the majority party, so unless they want to bolt to the Democratic side of the aisle -- as Rep. Michael Forbes of Long Island did this week -- they say they have to make compromises.

"There's a frustration about that, no question about it," said Rep. Jack Quinn (R-N.Y.), a moderate from a heavily Democratic district around Buffalo. "But we've got a very diverse caucus with a very slim majority. It's obviously hard to keep everyone happy."

The moderates say there is another reason for their cave-in reputations: They tend to be pragmatic split-the-difference types, and they're negotiating with committed ideologues. At one point yesterday afternoon, a GOP leadership aide expressed surprise that the moderates were still standing firm: "They're holding out a lot stronger than we thought they would."

But late in the afternoon, the moderates apparently dropped their objections. And even before they joined the team, they were taking pains to point out that they knew their leaders were in a difficult position, that they were anxious to work out a compromise.

"That's what moderates do -- they tend to be moderate, not extreme," said Rep. Amo Houghton (R-N.Y.), another opponent of the tax bill. "They're willing to compromise. It's sort of a condition with moderates. The problem is we deal with people who don't feel that way, and then one day you look in the mirror and say: Why am I the only one compromising?"

In fact, moderates were not the only ones complaining about the GOP bill yesterday. The leadership also had to worry about conservative members and pro-family groups angry that the bill does not eliminate the tax penalty many married couples pay. But the leaders assured conservatives that the House tax bill provision addressing the marriage penalty would be beefed up when it reaches a conference with the Senate. Across the Capitol, the Senate Finance Committee approved its version of the GOP tax bill on a 13 to 7 vote, with Democrats John Breaux (La.) and Bob Kerrey (Neb.) joining 11 Republicans in favor. Although the Senate and House versions are of comparable size and offer tax breaks for education, health care and businesses, they differ significantly in key details.

While the focus yesterday was on taxes, House leaders and appropriators continued to meet on a separate but related issue of how much to fund major spending programs in the coming year. Tax-cutters are attempting to claim most of the anticipated budget surpluses, while members of the Appropriations Committee insist that much of it is needed to fund crucial spending bills for labor and health programs and veterans-housing bills.

Rep. John Edward Porter (R-Ill.), chairman of the labor-health appropriations subcommittee, has drafted a bill that assumes he will get additional funding. Porter's tentative budget plans called for an 8 percent increase in spending for the National Institutes of Health, to $16.9 billion, and a slight increase in the $33 billion spent on education programs this year. Porter also wants to provide a small increase for the preschool Head Start program and maintain stable funding for the low-income home heating program.

But for now, those plans are on hold. Porter's committee indefinitely postponed a planned mark-up on the bill, as leaders continued to search for ways to fund the proposal within existing budget limits.

Staff writers Stephen Barr, George Hager and Dan Morgan contributed to this report.

CAPTION: Senate Budget Committee Chairman Pete V. Domenici (R-N.M.) displays chart during news conference in which he disputed White House figures on tax cuts and budget surpluses.