Only a day after Congress approved a plan for nearly $280 billion in deficit reductions over three years, key figures in both houses expressed doubt that all the debt savings will be achieved.

Although the budget compromise claims deficit reductions of more than $55 billion for next year, Senate Majority Leader Robert J. Dole (R-Kan.) and House Budget Committee Chairman William H. Gray III (D-Pa.) said the actual savings will be closer to $40 billion.

Gray, expressing a widespread feeling in Congress, acknowledged that economic projections and the budget's standard of measurement for defense cutbacks were probably misleading, contributing to an overly optimistic estimate of savings.

Dole questioned the results from another angle, expressing doubts about congressional enactment of the cuts it pledged.

"I think we have to be very careful when we look at numbers," he said, "because I doubt Congress will do all the things we've been asked to do, and the deficit will really be much larger than anticipated . . . . "

Dole, interviewed on NBC's "Today" show, did not say where Congress might fall short of its goals but later told a reporter the failure could occur in a wide variety of appropriations accounts, especially areas where authorizing committees are not ordered to make program cuts.

Other sources have cited likely resistance to the budget's proposed cuts in farm supports, Medicare and a variety of other smaller programs, including such popular ones as Amtrak and local economic development aid.

If Dole and Gray are correct, next year's deficit could be $180 billion or more, compared with $210 billion anticipated for the current fiscal year. By fiscal 1987, it could be more than $220 billion if current spending practices were continued without cutbacks.

Senate Budget Committee Chairman Pete V. Domenici (R-N.M.) observed late Thursday night that savings claimed for fiscal 1987 and 1988 are likely to be $25 billion to $40 billion less than anticipated, largely because economic assumptions on which the claims are based may be too optimistic.

This could mean a deficit of $150 billion by fiscal 1988, when the White House and congressional leaders had hoped to cut it below $100 billion. A separate analysis by Senate Democrats, based on earlier Congressional Budget Office economic assumptions, put the fiscal 1988 deficit at $161 billion.

These post-mortem assessments by three of the main figures in the seven-month congressional budget ordeal underscore the shakiness of figures used in the calculations, the fragility of economic assumptions that underlie the savings claims, and doubt about Congress' will to enforce the spending cuts it voted for Thursday night.

Part of the savings come from money that probably wouldn't be spent anyway or from using questionable benchmarks for measuring the savings.

Defense is a primary example. For a variety of reasons, the Pentagon does not actually spend all the money it could in a given fiscal year. These "savings" are added to more legitimate deficit reductions that result from restraining the growth of defense spending authority. But even the real savings depend on whether program cuts are measured against congressional projections or President Reagan's own spending plans, an accounting game that has gone on throughout this year's budget fight. Nearly $13 billion of next year's estimated deficit reductions are the result of using Reagan's, rather than Congress', benchmark.

Economic uncertainties are particularly important in projections for future years, making long-term savings forecasts extremely dubious.

For instance, by relying on economic projections by the CBO that are less rosy than those of the administration's Office of Management and Budget, Senate Democrats came up with $76 billion less in reduced deficits over three years than Senate Republicans did using OMB projections.

Even though both houses used the OMB figures, many lawmakers of both parties say privately if not publicly that the CBO is probably closer to the mark.

As for meeting the spending-cut targets, farm program plans now under consideration fall short of the budget's target numbers, as does Medicare reform legislation.

First-year savings can be enforced through appropriations ceilings imposed by the budget, but future savings are more difficult to achieve unless the programs themselves are cut through so-called "reconciliation" orders contained in the budget. Only about one-quarter of the projected three-year savings stem from permanent changes in law, although the final figure is double what the House originally proposed.

Budget negotiators, for instance, did not mandate program cuts for Amtrak, mass transit and a number of other politically popular programs, raising questions as to whether about $10 billion in future savings will be realized, according to a Senate budget source.

The negotiators dropped some of the most egregious examples of spending cuts that would probably never be made. These included such things as assumed savings from reforms of federal contracting practices and user fees that were unlikely to be enacted.

But billions of dollars are tied up in proposals that, regardless of budget mandates, may still not be approved.

In a statement yesterday about passage of the budget, Reagan threatened to use his "veto pen" to enforce spending restraint in the budget. But there is doubt within administration as well as congressional circles about how well this will work, especially without the expertise and legislative savvy of recently resigned OMB director David A. Stockman.

Reagan has seldom used a veto against appropriations bills but, through Stockman, has been successful in using veto threats to ratchet down spending in bills before they are passed.

Although the administration at various times asked Congress to kill more than 20 federal programs or major agencies to save money as part of the budget process, the House-Senate budget agreement assumes abolition of only four, House and Senate Budget Committee staff aides said yesterday. It is conceivable that legislative committees may move to kill other programs later, but that is not assumed in the budget agreement.

The four are federal payments to Conrail, which the government is selling; general revenue sharing, to be eliminated after 1986; the U.S. Travel and Tourism Bureau, and a small loan-guarantee operation under the Community Development and Block Grant program.