House Republican leaders mounted a campaign yesterday to give President Reagan about half the appropriations cuts he wants for this year and thus avoid a veto of the huge stop-gap spending bill Congress must pass by Friday to keep the government from running out of money.

Aides to Minority Leader Robert H. Michel (R-Ill.) said Michel will wage a floor fight Monday in the Democratic-controlled House to cut the so-called "continuing resolution" for the government by about 5 percent across the board.

They said this would be enough to save $3 billion to $4 billion of the $8.4 billion in domestic appropriations cuts that Reagan wants for fiscal 1982.

Asked if this would be enough to satisfy the White House, a spokesman for Michel said, "We haven't had any indication to the contrary" in conversations with administration officials.

The likely outcome of Michel's effort is unclear. One Michel aide acknowledged the Republicans face an "uphill" fight. Republicans, supported by conservative Democrats, won impressive victories for Reagan last summer on budget and tax cuts, but more recent votes on money bills have indicated some erosion of his support in the House.

The continuing resolution is necessary because no appropriations bills for the current fiscal year have been enacted, although some are nearing final approval.

As drafted by the Appropriations Committee and cleared yesterday by the Rules Committee, the continuing resolution would fund government agencies at levels considerably higher than Reagan wants until appropriations bills for those agencies have been adopted, or, if bills are never passed, until the end of the fiscal year on Sept. 30, 1982.

According to Republican congressional sources, the administration wants the continuing resolution to last only until March 30. But the Republicans will go along with the Democrats on a full-year bill, the sources said.

In outlining his plan before the Rules Committee, Michel said the spending cuts are necessary to "avoid a presidential veto" of the bill. Reagan has vowed to veto "budget-busting" money bills, although he has not said specifically what would be acceptable in the continuing resolution.

Congress is not expected to pass the measure until Nov. 20, when the current continuing resolution expires. If the new bill were vetoed, the government could be in a financial crisis the next week because technically it would be without funds to continue operating.

While Republicans in the House were trying to accommodate Reagan, GOP members of the Senate Budget Committee continued pushing a plan, opposed by Reagan, to balance the federal budget by 1984 through a $160 billion combination of tax increases and spending cuts.

A vote was put off until Monday, with the outcome apparently hinging on one or two senators. All but two of the committee's Republican majority have lined up behind the plan, which was drafted by Committee Chairman Pete V. Domenici (R-N.M.) as part of the Senate's version of a second budget resolution for fiscal 1982.

While it was waiting, the committee unanimously approved a "sense of Congress" resolution calling on Reagan to submit a plan "as soon as possible" to help curb interest rates, unemployment and inflation and produce a balanced budget by 1984.

Before passage, however, it was watered down by removing any mention of action this year. Reagan said earlier this week that he wants to defer major budget policy decisions until he submits his new budget in January. Consequently, any mention of action this year would have been embarrassing to the administration.

Meanwhile, the White House, seeking to forestall a Senate budget rebellion and recover from the controversy over Office of Management and Budget Director David A. Stockman's comments about the conduct of economic policy, circulated a memorandum reasserting its hold-the-line stance on spending and promising major budget decisions shortly.

It said Reagan expects to make "final decisions on nearly all aspects of the 1983 budget" within the next six weeks and called on agencies to continue living within their slashed-back levels.

"This budget will reflect my firm commitment to hold down government spending and reduce the serious adverse effect that government spending and government-stimulated borrowing is having on the national economy," the memo said. While "good progress" has been made, there is still "a long way to go," it added.