The Carter administration has acknowledged that the $15.8 billion fiscal 1981 deficit the president projected in his budget message six weeks ago actually will be at least $20 billion and could climb higher if spending is not cut.

The $20 billion figure was conceded by top Carter economic officials during budget-cutting talks this weekend with key House and Senate Democrats. The estimate is in line with that now being used by congressional budget experts.

The higher deficit means lawmakers now will have to cut more than the $20 billion or so thought necessary to balance the fiscal 1981 budget when the red ink figures had been estimated at $15.8 billion.

The reason is that cutting the budget also dampens the economy and reduces tax revenues the government expects to take in. Spending cuts almost always must exceed the size of the deficit if the budget is to be put in balance.

The higher estimate reflects two major factors -- recent increases in Defense Department fuel costs and other programs, and rising interest costs as a result of the recent tightening of credit by the Federal Reserve Board.

The Congressional Budget Office estimated last week taht the deficit for Carter's January budget would total $24.6 billion. However, that figure included several bills still in the hopper. Not counting those measures, the CBO figure is about $20 billion.

Carter proposed a budget of $615.8 billion, in January, but the White House has just revised that to between $624 billion and $625 billion, with revenues expected at just over $604 billion. The administration also is updating its economic forecast to show a shallower recession and higher inflation.

The developments came as House-Senate negotiators continued talks with Carter's top economic advisers on how to balance the fiscal 1981 budget, but fell short of reaching formal agreement on specific spending reductions.

The two sides have been meeting in marathon sessions since Thursday, and plan to resume their talks this morning in an effort to achieve a consensus on what spending cuts Congress would be likely to approve.

Although participants declined to comment publicly on the closed-door sessions, sources said the group has endorsed some $5 billion in money-saving proposals Carter included in his January budget -- a first step to ward holding the line on the deficit.

Most of these money-saving proposals -- which range from cutting impact aid to education to enacting Carter's hospital cost containment plan -- have been rejected by Congress in previous years.However, the deficit would climb to $25 billion to $30 billion if they are not approved.

Sources say the lawmakers also are exploring the possibility of recommending several billion dollars' worth of revenue-raising measures, from increasing taxes on cigarettes and alcohol to imposing import fees on foreign oil.

However, the legislators are said to beleive voters will not tolerate more than a few billion dollars in revenue-raising actions of any sort, meaning there will have to be substantial reductions in spending if the budget is to be balanced.

Carter has said he wants to balance the budget as a signal taht the governement is serious about fighting inflation. Studies done with computer models generally show that reducing spending by $20 billion or so would trim only 0.1 to 0.2 percentage points from the inflation rate.