The budget agreement worked out between the White House and key Senate Republicans is a fragile compromise that appears short of the votes it needs for passage in the Republican-controlled Senate.

President Reagan and the Senate GOP leadership have at least a week to line up a majority, but administration officials acknowledged last week that they have an uphill battle, even among the 53 members of the president's own party.

When the package emerged on April 4, Senate Majority Leader Robert J. Dole (R-Kan.) called it a "starting point" and said it had a "long way" to go.

And last week, Office of Management and Budget Director David A. Stockman predicted the budget fight would be the "legislative battle of the decade."

Democratic leaders said last week that few, if any, Democrats are likely to support the package. The Democrats are not expected to offer an alternative, but instead will push amendments to restore their favorite spending programs and test Republican strength.

Dole said he expected 40 or more such restoration amendments to be offered. Senate officials said the leadership and administration will work hard to defeat any amendment because once one succeeds "you open the floodgates and you won't have any package left."

Administration officials said last week they are hoping that concern over the annual federal budget deficit, which under Reagan has grown from less than $100 billion to more than $200 billion, will persuade GOP senators to stay in line against amendments for the sake of the whole package.

"If you're up for reelection in '86 it's tough to vote to cut some of those programs," said one official. "But can you vote against a sound economy? How many of them are going to want to take responsibility for killing the package?"

The agreement, expected to come before the Senate next week, would cut the deficit by $52.2 billion next year by eliminating or sharply scaling back many domestic programs, limiting the cost-of-living adjustments for Social Security and other benefit programs, and slowing the growth of defense spending.

But all of these have vocal constituencies that make cutback agreements difficult.

"I've been out taking the pulse of Pennsylvania and I'm getting a lot of concern from students on scholarships, from local officials on revenue sharing, from veterans on veterans' programs," and from senior citizen groups about Social Security, said Sen. Arlen Specter (R-Pa.), who faces reelection next year. "The budget poses real problems for me on many items."

The largest troublespot in the budget compromise, officials said, is Social Security.

The compromise proposes holding the annual cost-of-living adjustment (COLA) for Social Security and other benefit programs to 2 percent less than inflation, while guaranteeing a minimum increase of 2 percent.

Many Republicans, especially those running for reelection in 1986, are concerned about the political repercussions of limiting Social Security, especially after Reagan promised during his reelection campaign not to touch the program in any deficit-reduction plan.

In a representative comment, an aide to Sen. Alfonse M. D'Amato (R-N.Y.) said D'Amato "feels a commitment was given and we shouldn't be in the business of breaking promises."

Senior citizens' lobbying groups intensified the pressure on lawmakers during the Easter recess last week, approaching several senators, including Slade Gorton (R-Wash.), Charles E. Grassley (R-Iowa), and Bob Packwood (R-Ore.), and demanding that they vote against the Social Security limitation.

Democratic officials on the House side have already drafted a mass mailer to senior citizens that accuses Reagan and the GOP of deceiving voters on Social Security. A similar charge helped Democrats reclaim more than two dozen House seats in 1982.

The elimination of Amtrak, Urban Development Action Grants and mass transit subsidies and revenue sharing for local government has drawn fire in particular from northeastern lawmakers.

Several of them have said they will offer amendments to reverse the cuts.

Farm-state senators indicated last week that, although the compromise reduces farm, rural and feeding programs less than Reagan's original 1986 budget proposal, the cuts still are not acceptable.

The elimination of the Small Business Administration, tightening of student aid, and cuts in Medicare and other health programs also have drawn criticism and promises of amendments.

At same time, the growth in the Pentagon's budget agreed to in the compromise has been criticized by Republicans and Democrats alike.

Grassley, who is pushing an across-the-board freeze as an alternative to the budget compromise, said "there's too much there for defense" at a time when other programs are being killed or drastically scaled back.

A Senate GOP official acknowledged that the defense increase "is a big, big problem." There will be a strong push to reduce that increase, the official said, and if it is successful it is possible that Reagan would abandon his support for the package.

The administration in its 1986 budget request had proposed a 6 percent after-inflation growth in defense funds.