The White House last night accepted a small across-the-board spending cut in federal agencies, giving congressional Republicans the one, largely symbolic concession they had insisted be included in a final budget deal.

Until this week, President Clinton had vigorously opposed such an approach, dismissing it as "mindless" and destructive fiscal policy. But in two telephone conversations Tuesday night with House Speaker J. Dennis Hastert (R-Ill.), the president expressed a willingness to go along with a tiny cut as long as he is given "maximum flexibility" to manage the reductions himself, according to lawmakers and administration officials.

The concession removed the last substantive obstacle to a deal on the budget for the federal government, and late last night Senate Budget Committee Chairman Pete V. Domenici (R-N.M.) and White House officials confirmed that a deal had been struck.

GOP leaders had demanded the small across-the-board cut as a way of pressuring agencies to cut wasteful spending, and with Clinton now on board, House leaders prepared to ram a final agreement through their chamber today.

"We have reason to believe that we will have enough votes to pass it in the House and Senate and get it approved by the president," House Appropriations Committee Chairman C.W. Bill Young (R-Fla.) said yesterday evening.

But in the chaos of the final days of the session, White House and congressional negotiators haggled through the night before agreeing on the precise language of the across-the-board cut. And furious maneuvering over last-minute efforts to load up the measure with special-interest measures--including a GOP provision overturning a new Agriculture Department milk pricing plan--has complicated the politics and virtually ensured a prolonged debate in the Senate.

With budget talks dragging on seven weeks beyond the start of the new fiscal year, the prospects for swift congressional passage of a final deal before Thanksgiving appeared dim.

Clinton has signed eight of the 13 annual federal spending bills into law, and the two sides have essentially agreed on what will go into the rest, to be combined into one giant $400 billion bill. The president will get extra money for hiring teachers and police officers, and for a key environmental initiative, while the Republicans will get their across-the-board cut. The two sides also agreed to include $12.8 billion to restore the cuts in Medicare that were ordered two years ago.

In an important sign of Democratic support for the plan, House Minority Leader Richard A. Gephardt (D-Mo.) told reporters that he expects to vote for the budget bill, saying, "I think in balance there is more favorable than unfavorable."

But in the Senate, the politics were more complicated. Sens. Herb Kohl (D) and Russell Feingold (D) of Wisconsin and Sens. Paul D. Wellstone (D) and Rod Grams (R) of Minnesota, who represent major midwestern dairy states that would be disadvantaged by the proposed milk provisions, have vowed to employ parliamentary tactics to block the spending bill.

Senate Majority Leader Trent Lott (R-Miss.) defended the dairy measure, saying it reflects "the needs and desires" of House and Senate members from the Northeast. "And if some senator feels that he must, you know, delay it, or filibuster, then you just have to deal with that," Lott said.

For example, late last night, the spending bill was redrafted in a way that would frustrate efforts by Kohl and others to prolong the Senate debate by insisting the entire bill be read, according to appropriations aides.

Across Capitol Hill yesterday, lawmakers scrambled to hitch unrelated, but important, legislation to the must-pass budget deal. Congressional leaders, for instance, agreed to add a major bill giving satellite television owners the ability to receive local network signals--but only after deleting two controversial provisions.

One of the deleted measures would have specifically denied Internet companies the same rights that cable companies have to automatically retransmit programming. Under an agreement accepted by Hollywood studios, sports leagues, cable companies and Internet service providers, an accompanying report will make clear that Congress has not yet ruled on the issue.

The second provision would have offered as much as $1.2 billion in federal loan guarantees as an incentive for satellite companies to provide local service to rural areas. Senate Banking Committee Chairman Phil Gramm (R-Tex.) vowed to block the bill if it contained the provision, which he attacked as "corporate welfare." But Gramm agreed to hold hearings on the rural problem by April 1 and to quickly move legislation to deal with the problem if necessary.

Sources warned, however, that the move to drop the guarantees could drain support in the House for the overall spending bill.

GOP leaders also agreed to attach language exempting scrap metal recyclers from liability for costs related to cleaning up toxic waste sites. The companies' association, the Institute for Scrap Recycling Industries, is represented in Washington by Haley Barbour, former chairman of the Republican National Committee, and former representative Al Swift (D-Wash.), who was a key supporter of legislation for cleaning up toxic waste sites while serving in Congress.

The provision is opposed by many business groups on grounds that the exemption will push the clean-up costs onto others. But the rider has the backing of Lott, a longtime friend and political ally of Barbour's.

The scrap rider is "not only on the table, it's in the grain of the table itself," said Sen. Larry E. Craig (R-Idaho).

However, GOP leaders anxious to avoid new controversies rejected an effort by seven midwestern and southern utility companies to get temporary relief from recent enforcement actions by the Environmental Protection Agency.

And Hastert said the spending bill would not include controversial language, being promoted by Sen. Robert C. Byrd (D-W.Va.), to allow coal mine operators in his state to continue dumping debris into rivers and streams despite a recent court ruling against the practice.

But the leadership last night was preparing to drop in dozens of other projects and special-interest provisions at the last minute to satisfy the demands of members, according to GOP aides and the administration.

The focus of much of the behind-the-scene activities was on how to structure the across-the-board cut. The 0.38 percent cut that Clinton, traveling in Turkey, discussed with Hastert Tuesday night would produce about $1.5 billion in savings--a relatively small amount by federal budget standards but enough for Republicans to cite in their crusade to avert the spending of any Social Security tax revenue. Under the more flexible approach discussed, the administration could target certain programs for cuts while protecting others deemed more important. No program or account would suffer a loss of more than 5 percent of its new funding under this approach.

In return, the White House and many Democrats are insisting on an additional $100 million for legislation that would allow disabled workers to keep their government health benefits if they take jobs. That legislation might also be attached to the spending package.

Staff writer Helen Dewar contributed to this report.

CAPTION: White House Budget Director Jacob "Jack" Lew, left, huddles with Sen. Herb Kohl (D-Wis.).