President Reagan's hopes for big new cuts in domestic spending faded even further yesterday as the Republican-controlled Senate Appropriations Committee took only a relatively small nibble out of its $84.9 billion money bill for health, education and other social services.

The military end of the budget got jacked up, too, as the Senate added $300 million for nuclear weaponry to a money bill for energy and water projects that Appropriations Chairman Mark O. Hatfield (R-Ore.) warned would now be about $700 million more than Reagan wants. The bill was passed last night, 71 to 22.

The actions came as Senate and House Republican leaders were invited to the White House today for their long-awaited meeting with Reagan on possible compromises in his latest budget proposals, which the leaders have said cannot be passed in their present form. The House Budget Committee joined its Senate counterpart in putting off further action on the budget until after Reagan's plans are made known.

The Appropriations Committee action gave the latest of many signals that Congress, which has already voted deep cuts in social programs, is unlikely to give Reagan much more than half the $13 billion in additional spending cuts that he wants this year to hold down the budget deficit.

Thwarted in an attempt to cut $2.6 billion from entitlement programs as well as discretionary spending, Republicans on the committee settled for cuts totaling $493 million from an earlier subcommittee draft of the bill and spent the rest of the day trying to keep the savings intact.

They were only partly successful. By the end of the day, the committee had restored $223 million, leaving net savings of $270 million.

Even with the cuts, Sen. Harrison Schmitt (R-N.M.), chairman of the subcommittee for labor, health and human services, warned that the bill is "very vulnerable" to a presidential veto, perhaps more so than any others. The $84.9 billion bill is roughly $1.6 billion more than the $83.3 billion that Reagan proposed in September in calling for a second round of budget cuts. The House has approved $88.2 billion for the same programs. Schmitt said yesterday it will be a "Herculean task" to keep a final congressional compromise to within $2.5 billion more than Reagan wants and asserted that the excess could reach as high as $3.5 billion.

The social services appropriation is second in size only to the defense bill. Most programs were already cut severely before the committee attempted to accommodate Reagan's September goal of a 12 percent cut from his March budget.

Schmitt and others contended that opportunities for further cuts were limited by the fact that nearly three-quarters of the money goes to entitlement programs like Medicaid and Medicare that are controlled by other committees. Schmitt had hoped to cut entitlement programs by $2 billion but ran into objections from Finance Chairman Robert J. Dole (R-Kan.) and others--objections so strong that he abandoned the effort.

The proposal for $493 million in additional cuts, made by Schmitt, was approved after Sen. Lowell P. Weicker Jr. (R-Conn.), joined by most Democrats on the committee, attempted unsuccessfully to add $970 million to the original bill. Weicker failed, 10 to 5, but he and his allies continued to press for add-backs, item by item.

Even Schmitt appeared reluctant in his opposition to many of the proposed restorations. "I don't like to oppose these programs," he said at one point. "They deal with very real needs. But we have to find a balance."

The committee's Republican majority, joined in most votes by some Democrats, succeeded in fending off most of the proposals, including a move to restore $200 million for low-income fuel assistance--over objections from Weicker that "people will die" this winter for lack of ability to pay fuel bills. Among the restorations that the committee approved were $107 million for Public Health Service hospitals, $20 million for community health centers, $50 million for the community services block grant, $25 million for student aid and $3 million for drug and alcohol programs.

The extra $300 million for nuclear weapons was approved by the Senate, 49 to 43, after Armed Services Chairman John Tower (R-Tex.) agreed to reduce his original proposal of $500 million to get the votes of some wavering senators, including Budget Committee Chairman Pete V. Domenici (R-N.M.).

Hatfield adamantly opposed the Tower effort, noting that nuclear weapons spending had already been increased $1 billion, or 30 percent, this year.