In the summer of 1981, a discouraged Office of Management and Budget Director David A. Stockman told journalist William Greider, "I have a new theory -- there are no real conservatives in Congress."

Stockman had just watched Congress accept many of President Reagan's recommended cuts in welfare-state programs but turn down most of the proposed reductions in middle-class entitlements and business subsidies.

Four years later, Stockman is testing that theory again by sending up a new Reagan budget asking lawmakers to reduce or eliminate dozens of programs used by their most vocal and important constituents.

The new budget puts the Republicans on the spot.

From farm supports to commuter rail subsidies, from veterans' benefits to export aids, Reagan and Stockman have targeted many of the mainstream domestic activities of government that have been protected by bipartisan majorities in Congress for decades.

"There's no question," one senior White House aide said last month, "this budget goes at the heart of Republican constituencies."

As Reagan and Stockman set out to butcher these "sacred cows," some wonder if it is not the Republican Party that is being led to slaughter.

Sen. John Heinz (R-Pa.), who as chairman of the Republican Senatorial Campaign Committee, has a special interest in the fate of his 22 Republican colleagues running next year, said the Reagan budget proposal puts GOP legislators "between a rock and a hard place."

Heinz said Secretary of Defense Caspar W. Weinberger's "intransigence" forced Stockman to recommend "unrealistically deep cuts and program eliminations in literally dozens of areas."

Speaker of the House Thomas P. (Tip) O'Neill Jr. (D-Mass.) underlined the point with his comment that "the administration budget released today sends a tough message to the American middle class. Past Reagan budgets have hit hardest at the poor. This budget . . . takes the pain of budget-cutting directly to middle America."

Democrats set out to publicize the pain by scheduling grass-roots hearings on the proposed budget cuts. Meantime, Rep. Tony Coelho (D-Calif.), chairman of the Democratic Congressional Campaign Committee, said the rift among Republicans about the proposed cuts "may not help us, but it hurts them at a time when we are vulnerable."

Republicans have been increasingly optimistic about their long-term prospects, with voter preference polls showing a steady narrowing in the Democrats' traditional lead. But the budget dilemma -- the choice between tolerating deficits that could trigger a new round of inflation and recession or accepting the political consequences of cutting popular programs -- presents a real danger to those who must run in 1986.

While Heinz's comment capsulizes the anxiety many Republicans feel at the stiff domestic cuts Reagan is recommending, he and others suggest there may be a way of turning the problem to their advantage.

From moderates like Senate Budget Committee Chairman Pete V. Domenici (R-N.M.) to conservatives like Rep. Tom Loeffler (R-Tex.), Republicans argued that Reagan had staked out two political strongpoints around which his party could rally.

By establishing the goal of freezing program expenditures at $804 billion, Domenici said, the president "has set a target that is clear and significant for the layman -- no higher spending." And by ruling out a resort to higher taxes, Loeffler added, "The president has reinforced the position taken by the Republican Party in our platform and endorsed overwhelmingly by the American people last November."

The initial congressional reaction suggested that the most controversial feature of the budget was Reagan's insistence on letting defense spending grow 13 percent, while many domestic programs were being trimmed or eliminated.

The harshest comment came from a key Republican, Senate Appropriations Committee Chairman Mark O. Hatfield of Oregon. "It is unfortunate indeed that Congress must dissipate its energy confronting a strategy which obviously seeks to achieve the highest possible defense figure, rather than a responsible compromise," Hatfield said.

"The base is much too narrow," Heinz agreed. "We need to broaden it to include everything except the interest on the national debt, even if that's not what the president wants."

Such comments led Sen. George J. Mitchell (D-Maine), chairman of the Democratic Senatorial Campaign Committee, to predict that "the Republicans who are running for reelection next year will run away from the budget."

Nonetheless, Domenici predicted that he would be able to get "consensus" on a package of domestic cuts from his committee, which includes six senators facing reelection next year, and then use that agreement in a final attempt to wring concessions from Reagan, Stockman and Weinberger, including a freeze on Social Security cost-of-living allowances and a reduction of the defense buildup.

His optimism was questioned by some other top Republicans. Rep. Dick Cheney (R-Wyo.), chairman of the House Republican Policy Committee, said most Republicans realize that the administration's domestic cutback proposals "are not there because they desire to do it; they were driven to that particular portion of the budget by their decisions not to do Social Security, or touch defense or raise taxes."

Cheney said he supported many of those cutbacks, but predicted "they will run into a lot of political difficulties up here. There are people here who feel they have a bigger stake in some of these 'sacred cows' than the president does; they helped breed them."

Cheney's warnings were underlined by a prominent Republican pollster, heavily involved in advance planning for the 1986 campaign.

"The budget is a freebie for the president," he said, "because the public overwhelmingly believes that control of spending is in the hands of Congress. But if you're a Republican senator running in a tough state, you've got to be looking at this process with a good deal of anxiety."

Predicting the president will be less persuasive with Congress than he was in 1981, he said, "It's a very different atmosphere than it was after his first victory. You find a lifeboat mentality among the Republicans running in 1986, and they don't think the president is in the same boat."