The Reagan administration called yesterday for speedy, prepackaged handling of its spending cut proposals as congressional leaders, while differing over tempo, agreed the job could be done by summer.

House and Senate Democratic leaders concluded they lacked the votes for an all-out fight against the administration's $41.4 billion in spending cuts for fiscal 1982, and decided on a strategy of selective opposition to specific proposals.

Democratic budget leaders in both houses -- House Budget Committee Chairman Jim Jones (D-Okla.) and Sen. Ernest F. Hollings (D-S.C.) -- said they thought the administration may be able to win approval of about $30 billion in cuts.

Democrats as well as Republicans see President Reagan riding the crest of strong public demand for spending retrenchment, and for now at least, many Democrats are fearful of being labeled obstructionist if they resist him. m

But there were also indications of at least some trouble for both the tax and spending cut proposals that Reagan laid before Congress on Wednesday night.

Labor leaders and blacks yesterday called Reagan's spending cuts unfair to the poor and the United Mine Workers threatened a strike to defend threatened black lung benefits.

In their first appearances on Capitol Hill since details o the program became known, administration officials ran in into skeptical if not hostile questioning from senators of both parties, extending even to Reagan's sense of commitment to his own program.

And Senate Majority Leader Howard H. Baker Jr. (R-Tenn.) said Reagan's proposed 30 percent tax cut over three years might be even harder to pass than his recommended spending cuts, possibly taking until next year to complete and then in a form that may well differ from what Reagan asked for.

Many Democrats, and some prominent Republicans as well, complain that the proposed cut is too large, inflationary and tilted toward the rich, whom Reagan is counting on to invest the windfall to stimulate productivity. Some are also leery of letting Congress pass a tax cut without locking itself into enough budget cuts to keep the deficit from rising to politically untenable levels. Also, some Democrats fear that a big tax cut will increase pressure for cuts in their favored domestic spending programs.

In the Republican-controlled Senate, Reagan's spending cut proposals were put on a super-fast-track by Baker, who said he wanted the Senate Budget Committee to report out a set of spending cut instructions within a week to 10 days and the Senate as a whole to act on it within a month or less. This is a much speedier schedule than he outlined Wednesday and appeared to hinge, precariously, on the administration's ability to produce the detailed information that the committee needs before it can act.

"Every day this is delayed makes this [the cuts] more difficult to pass," Baker told reporters.

But the Democratic-controlled House embarked down a considerably more deliberate course, even though House Speaker Thomas P. (Tip) O'Neill Jr. (D-Mass.) and Budget Committee Chairman Jones said it was aimed at producing an agreed-upon group of budget cuts by the congressional August recess.

The vehicle chosen for the cuts by Baker and Jones -- and endorsed yesterday by David A. Stockman, Reagan's budget director and principal author of the economic program -- is a rarely used budget control process known as "reconciliation." Under this procedure, used last year to get $8.2 billion in program cuts and revenue increases, congressional committees are directed to cut programs to achieve specific savings under a fixed deadline.

"The Congress has at its disposal a tool under the 1974 budget act that can permit the president's reduction proposals to be considered rapidly and as a package," Stockman told the Senate Budget Committee. "I urge this committee and the Senate to begin as soon as possible. . . ."

Senate Budget Committee Chairman Pete V. Domenici (R-N.M.) said some of the recommended $41.4 billion in spending cuts, such as those involving merger of some existing grant programs, will have to be handled separately but predicted that most of the cuts can be included in the reconciliation measure.

Domenici intends to push ahead with the spending cuts before starting on the first budget resolution for fiscal 1982, while Jones plans to mesh the two, which helps explain the slower pace in the House. House Democratic leaders have pushed for a more deliberate pace to permit consultation with turf-conscious authorizing committees, whose power could be seriously eroded in a blitzkrieg budget-cutting operation that is directed by the budget committees.

During the Stockman's appearance before the Senate committee, he was preppered with questions about specific cuts.

Domenici expressed concern that more economies were not proposed in foreign aid, low-cost housing and cost-of-living indexing for entitlement programs. Sen. Mark Andrews (R-N.D.) challenged his credit cutback proposals for rural electricification. Sen. Charles Grassley (R-Iowa) noted Reagan's reputation for acommodating Democratic lawmakers while governor of California and questioned whether he might do the same again in Washington. If Reagan starts compromising, then "nothing's going to be accomplished."

Stockman sought to assure Grassley that "you can count on the fact that we'll stick with the program."

Hollings expressed concern about the tax cut and anticipated budget deficits, which the administration concedes will continue until 1984, when it plans a balanced budget. "You can't tell me we don't need to worry about them, and that's why we're the minority party."

The predictable flurry of criticism from labor leaders broke the silence in which they had watched as Reagan put together his spending cut plan. However, Reagan told a group of newspaper editors at the White House the he believes the union heads are sometimes out of step with their own rank and file. They certainly were in the last election," Reagan said. Most unions backed President Carter but Reagan's appeal to traditionally Democratic union voters cut deeply into Carter's support in industrial states.

The 18-member Congressional Black Caucus criticized the Reagan program for hacking away at programs that "are the lifelines" for millions of poor people.

"Reagan is a reverse Robin Hood, robbing the poor and giving to the rich," Rep. Gus Savage (D-Ill.) said at a news conference.

Most of the criticism on Capitol Hill was of the tax cut, not the spending cuts.

Sen. Alan Cranston (D-Calif.) said that there is no way to be sure that the rich will invest their tax savings in ways of benefit to the economy. "They must just buy more fur coats and Cadillacs," he said.

Ways and Means Chairman Dan Rostenkowski (D-Ill.), who will control the movement of the tax cut through the House, has indicated he is skeptical of some of the underlying assumptions of the Reagan proposals.

One is how much growth the cuts will produce. In addition, Rostenkowski sees tax legislation in part as a means for adjusting the status of the wealthy, middle class and poor. Reagan does not.

The ranking Republican on Ways and Means, Rep. Barber B. Conable Jr. (R-N.Y.), has warned, however, that Rostenkowski will be accused of obstructionism if the tax bill languishes in the committee past April.

"There's no need for extended hearings. We all know what we're talking about," Conable said.