With a new denunciation of the federal "spending juggernaut," President Reagan yesterday sent Congress a revised fiscal 1982 budget containing $48.6 billion in spending reductions.

On Capitol Hill, however, even Republicans were already flinching from some of the proposed spending cuts. The GOP-diminated Senate Labor and Human Resources Committee went on record in favor of more spending than the president wants for education, aid to the handicapped, fuel assistance for poor people and black-lung benefits for coal miners.

[More than 6,000 miners marched to the White House yesterday to protest the plan to reduce the federal black-lung program.]

In recommendations to the Senate Budget Committee, which will begin action on Reagan's spending reduction plan next week, the Labor Committee also proposed reduced funding for the Legal Services Corp. but balked at snuffing out legal aid to the poor, which is what Reagan wants to do.

Neither the congressional prospects nor the attacks on his proposals by various groups of protesters that marched on the White House and the Capitol yesterday appeared to disturb Reagan's optimism.

On a gloomy day in the White House Rose Garden, Reagan joked with Office of Management and Budget Director David A. Stockman as he signed the budget document, then told an audience of OMB officials that the reductions "are a part of a longer-term program designed to stop inflation, reward enterprise and intitiative and put America back on the road to prosperity."

"As I've said many times, our ultimate goal is to make government, again, the servant of the people by cutting its size and scope and insuring that its legitimate functions are carried out efficiently and justly," Reagan said.

Reagan gave no details of the budget cut proposals that he said would add "hundreds of savings to the 83 major reductions that we announced on Feb. 18." But congressional sources said that among the new reductions, Reagan will announce that he is seeking only 175,000 units of additional subsidized housing for the poor in fiscal 1982, compared with the 260,000 in then-President Carter's Jan. 15 budget requests and 225,000 in the earlier Reagan budget proposal.

Reagan's appearance in the Rose Garden was frankly designed by White House aides to get him on evening television along with the critics of his budget on a day when the White House had nothing new to announce. Meeting with officials of the National Association of Counties on the eve of a two-day official visit to Canada, Reagan confessed that he was unfamiliar with a number of details in his own budget plan.

But Reagan did use the occasion of the meeting to revive, in unspecific form, an old idea for returning federal programs to state and local governments.

After assuring the county leaders that the savings in federal overhead in the block grants he is proposing would be enough to pay for the budget cuts in the programs, Reagan said:

"I have a dream of my own. I think block grants are only the intermediate steps. I dream of the day when the federal government can substitute for those the turning back to local and state governments of the tax sources that we ourselves have preempted here at the federal level so that you would have those tax sources."

Reagan also confirmed in this meeting that the administration is preparing legislation requiring "able-bodied" welfare recipients to work as a condition of their grants. His comments came at a time that groups of coal miners, blacks and city officials were in Washington protesting the already announced budget cuts.

The Senate Labor Committee, which has jurisdiction over many social welfare programs, did -- as expected -- go most of the way with Reagan in endorsing heavy domestic spending cuts. I voted to cut roughly $9 billion from the $50.4 billion that Carter proposed for health, education, job and social service programs, and rejected, on straight party-line votes, numerous Democratic efforts to restore many of the cuts.

But, in its reluctance to go all the way, the comittee underscored the difficulties that the Reagan administration may have in getting all it wants from Congress, despite the political support in both houses for deep and dramatic spending retrenchment. In all, the committee added about $2 billion to Reagan's spending proposals.

In education, the committee, at the recomendation of subcommittee chairman Robert T. Stafford (R-Vt.), endorsed spending reductions of 12 percent, as opposed to the administration's proposed 20 percent. Committee aides said the difference amounted to $1.3 billion.

On fuel assistance, the committee, with most Republicans going along, proposed no cut in the 1981 spending level of $1.85 billion.

The committee voted to retain $100 million for the Legal Services Corp., with only passing discussion of Reagan's proposed elimination of the program. On a straight party-line vote, however, the committee rejected a Democratic proposal to reinstate $289 million of the $346.5 million that Carter had recommended.

For black-lung benefits, the committee went along with a proposal by Sen. Jennings Randolph (D-W.Va.) to increase funding from $112.3 million to $149 million and to recommend an increase in the federal tax on coal tonnage to help finance the benefits.

For major programs for the handicapped, the committee proposed a 10 percent increase in spending, while Reagan had proposed a 20 percent cutback.