A bipartisan majority on the Republican-controlled Senate Budget Committee dealt President Reagan a stunning reversal last night in rejecting, 12 to 8, a spending blueprint for next year that was tailor-made for Reagan's economic program.

A few hours later, in a setback that was more predictable, the democratic-run House Budget Committee voted, 17 to 13, largely along party lines to approve a Democratic alternative to Reagan's budget -- although it was clear that the House Democratic majority also had problems with its proposal.

On the Senate committee, all Democrats joined Republicans William L. Armstrong (Colo.), Steven D. Symms (Idaho) and Charles Grassley (Iowa) in voting to reject the proposed budget for fiscal 1982 and try again after Easter recess.

Just a week ago, the Senate over-whelmingly approved instructions to legislative committees to carry out $36.9 billion worth of Reagan's spending cuts. But yesterday, its budget committee was faced not just with spending levels, but also with the administration's three-year, across-the-board tax cut and projected deficits for the next three years.

The Democrats objected to the tax cut; they also distrust Reagan's economic assumptions. The Republicans complained that the committee's proposal would not guarantee a balanced budget by 1984, as Reagan had promised, and demanded further spending cuts.

With skepticism in his own party about his economic program, as well as opposition from Democrats, Reagan now is faced with the distasteful choice of modifying his tax cut or slicing even deeper into his budget in order to get it to the Senate floor.

As it became evident that the budget would be defeated, committee Chairman Pete V. Domenici (R-N.M.) pleaded in vain for approval, saying, "For those of you who say you are for this president, this budget is his budget." But Sen. Daniel P. Moynihan (D-N.Y.) responded: "The Republicans promised miracles, and now they face reality."

"It's a setback, but it was unavoidable," said Domenici after the session. "It's temporary. It will bring a lot of people to their senses."

A spokesman for the Office of Management and Budget said "there is concern about the vote, but it 's not irretrievable. . . ."

Meanwhile, House Republicans, apparently in consultation with the White House, rallied behind a modified version of the Reagan plan that included a scaled-back deficit.

Rep. Delbert Latta (R-Ohio), ranking Republican on the budget committee, said the modification, rather than the original Reagan plan, will be introduced as the Republican proposal when the House takes up the budget after the recess.

The Senate panel vote to reject the resolution came shortly after the committee departed dramatically from the administration's budget script and voted to save nearly $8 billion next year by restricting cost-of-living increases for Social Security and other federal retirement programs.

Voting 9 to 8 to reverse a stand it took less than a month ago, the committee agreed -- as part of its budget blueprint for next year -- to abandon the consumer price index as the yard-stick for cost-of-living increases if consumer prices increase more than wages for the year. It also agreed to change the payment date for benefit increases from July to October, thereby saving three months' worth of costs.

With wages expected to rise less than prices, use of a wage index, coupled with a delay in the payment date, would save $600 million in 1981 and $7.8 billion in 1982, according to Sen. Ernest F. Hollings (D-D.C.), who has led the campaign for clamping down on the costly "indexing" of federal benefits as part of the overall effort to cut federal spending.

In all, it would save $38.4 billion by 1986, Hollings said. Major programs that would be affected include civil service and military retirement, railroad pensions and veterans pensions as well as Social Security.

With the administration actively opposed to any change in the indexing formula until its budget cuts are nailed down, Domenici had reluctantly opposed the change in previous votes both in committee and on the Senate floor. But he switched this time because, an aide said, he basically believes that federal spending cannot be controlled without clamping down on the big, costly entitlement programs like Social Security.

Hollings had the support of only one other Democrat, Sen. James Exon (Neb.), but was joined in the vote by seven Republicans: Domenici, grassley, Dan Quayle (Ind.), Symms, Robert Kasten (Wis.), Slade Gorton (Wash.) and Armstrong.

It was not immediately clear where the Senate committee's rejection of the budget left the issue of cost-of-living payments.

The possibility of raising another $7.8 billion, or perhaps more, by cutting into entitlement programs may become more attractive as the administration and its Republican congressional allies forage for ways to trim current and future budget deficits.

The Democratic majority on the House Budget Committee rejected the notion of tampering with Social Security as politically unfeasible without administration support, but some influential panel members like the idea.

The surprise Senate committee vote came as budget panels of both houses worked to complete separate versions of spending targets for fiscal 1982, with the Senate committee initially going down the line for Reagan's budget and the House committee opting for a somewhat different vesion drafted by its Democratic leaders.

The Democratic proposal shifted some defense money to social programs that Reagan proposed to cut and, scaling back the president's proposed tax cut, came up with a deficit smaller than the $45 billion deficit that Reagan forecast.

The resolution rejected by the Senate committee had recalculated Reagan's deficit at about $60 billion, although the savings from the cost-of-living changes had reduced the total deficit to $53.8 billion.

In action earlier yesterday, the Senate committee gave Reagan all he wanted for his big proposed increase in defense spending, while the House committee deferred until after the Easter congressional recess a show-down over the Democrats' original proposal for a $4.3 billion bite off the top of Reagan's huge proposed defense spending increase for next year.

As an apparent holding action, they agreed to accept the administration's estimate of defense spending costs, which differs from their own, thereby obviating -- for the time being at least -- the controversial cuts that had been proposed, including elimination of the July pay increase for military personnel.

But in a vote pitting Reagan's defense proposal against the Democratic alternative, the Democrats won narrowly. A move to endorse Reagan's failed, 14 to 14. Then the Democratic proposal was approved, 16 to 13.

The Pentagon spending figure is considered curcial to the Democratic leadership's chances to pick up enough conservative Democratic votes to carry their "alternative" budget when it comes up for a vote on the House floor in late April.

As of now, "I don't know of any package that can pass," said Budget Committee Chairman James R. Jones (D-Okla.), author of the Democratic counterproposal. "If everybody digs in their heels and says, 'Our package or none,' I don't think there are 218 votes [a majority of the House] for anything at this stage."

Rep. Bill Nelson (D-Fl.), a conservative, said he thought the committee could pick up the votes of 25 to 28 of the 44 members of the House Conservative Democratic Forum (caucus) if it agreed to restore $2 billion for defense. But some liberals warned that the committee would risk defections from the left. And Rep. Phil Gramm (D-Tex.), who advocated even greater cutbacks in domestic programs than the administration wants, said $2 billion would be enough.

In the Senate committee, a bipartisan coalition led by Domenici and Hollings fended off opposition from all sides in boosting Reagan's defense proposal, which they figured would cost $193.9 billion, or $5 billion more than Reagan calculates.

The vote was 11 to 9 in favor of Reagan's proposal after the committee rejected two efforts to scale it back and a move by Armed Services Committee Chairman John G. Tower (D-Tex.), also a budget committee member, to expand it by $600 million in outlays.