Democratic leaders in the Senate agreed with Repulbican leaders yesterday on a strategy for packaging and expediting $125.9 billion in budget savings that President Reagan wants over the next three years. Their plan is aimed at sending the package to Reagan for signature by June 30.

The agreement was contained in a largely symbolic resolution intended to express leadership sentiment and to keep the budget-cutting momentum going. Senate Budget Committee Chairman Pete V. Domenici (R-N.M.) and Sen. Ernest F. Hollings (D-S.C.) plan to introduce today the resolution that calls for program cuts sufficient to save $125.9 billion through fiscal 1983, which is what Reagan has asked Congress to do.

The package would include savings of $4.8 billion for the rest of fiscal 1981 and $41.4 billion in savings for 1982.

The resolution will be referred to the Budget Committee, which can modify it in preparing -- under the so-called budget "reconciliation" process -- a set of instructions to committees for specific program cuts. These instructions have to be approved by both houses, along with the eventual cuts the committees propose. The Budget Committee is reportedly considering cuts other than those recommended by Reagan.

A Budget Committee aide said leaders of both parties, including Senate Minority Leader Robert C. Byrd (D-W.Va.) as well as Majority Leader Howard H. Baker Jr. (R-Tenn.) pledged their "wholehearted cooperation" in getting the package through Congress as soon as possible. However, at least some Democrats, including Byrd, object to setting any timetable, although they insist they do not want to delay the measure. It was domenici who set the June 30 deadline.

House Democratic leaders, one of whom testily accused GOP congressional leaders of "playing politics" on the issues earlier in the day, indicated they would stick by their timetable, which anticipates completing action without the Senate's shortcuts by July 4. Although the Domenici-Hollings resolution is theoretically a joint resolution, there is nothing to prevent the House from ignoring it and marching to its own drummer.

Asked about Republican efforts to speed up consideration of the budget cuts package, House Speaker Thomas P. (Tip) O'Neill Jr. (D-Mass.) snapped, "We'd be a lot better off if the Michels [House Minority Leader Robert H. Michel of Illinois] and Bakers would quit playing politics and let us get down to work . . ." O'Neill said he had no complaints about Reagan. "It's the fellows on the fringes who are making all the noise," he added.

The scrimmaging on budget cuts came as the House Ways and Means Committee prepared to begin formal consideration of Reagan's tax cut proposals today and the White House continued its selling job on both the tax and spending cut initiatives.

In testimony before the Senate Government Affairs Committee, Office of Management and Budget Director David A. Stockman said he thought Congress should be able to finish with the tax cut bill by July 1. Later he told reporters that the administration wants it to wrap up both the tax and spending packages by its August recess.

In an interview with the Chicago Tribune, Stockman said the administration's second tax cut proposal, which will deal with reductions not included in the across-the-board cut of 30 percent over three years that Reagan proposed last week, will cost less than $10 billion and will not impede plans to balance the federal budget by 1984.

Stockman also had harsh words about federal regulators and consumer activits in the interview. Asked about the proposed elimination of the Federal Trade Commission's antitrust enforcement arm, Stockman said, "If you eliminated the FTC [itself], the world would never know the difference." Added Stockman, "The more money they have, the more regulations and interference they're going to generate."

As for consumer activists, he said, "They've created this whole facade of consumer protection in order to seize power in our society. I think part of the mission of this administration is to unmask and discredit that false ideology."

In a briefing by several Cabinet members for reporters. Transportation Secretary Drew Lewis said proposed meass transit cutbacks would not halt subways already under construction ("where there's already a hole") and added that, while no Conrail subsidies are planned after 1982, some way will have to found to keep the Northeast Corridor rail system in operation. But he called Amtrak an "economic disaster" and said only its most heavily used passenger trains should continue to be funded.

Agriculture Secretary John R. Block said proposed milk price supports will have to be cut back carefully so cities are not left with inadequate milk supplies. "We need to discourage farmers from keeping so many cows," but not at cities' expense, he said.

On Capitol Hill, Stockman also said he and Block sahre a "strong inclination" to eliminate farm deficiency payments under which farmers are compensated when market prices fall below established target prices for a commodity. Elimination of this program would save $90 million in 1982 and $647 million over five years, according to the Congressional Budget Office.

Meanwhile, the budget cut proposals continued to get a yes-but response in Congress. The latest came from Sen. Harrison Schmitt (R-N.M.), a former astronaut and now space subcommittee chairman, who rhapsodically embraced Reagan's overall budget cuts but added, "I have never seen any decline in public interest in space."