The Cabinet was told by Office of Management and Budget Director David A. Stockman yesterday that without further spending cuts or new tax increases next fiscal year, the federal budget deficit will balloon to between $185 billion and $195 billion.

This estimate, presented by Stockman in a closed meeting of the Cabinet and President Reagan, indicates the size of the problem facing Reagan in the next few weeks as he attempts to whittle down federal spending in the fiscal 1984 budget he will submit to Congress Jan. 17.

Because Reagan has ruled out any scaling down of planned increases in defense spending and does not want to increase taxes, Stockman's figures mean that domestic spending would have to be cut severely to reduce significantly the projected budget deficit.

The president has already decided to make "fairly sizable" trims in domestic spending next year, according to administration officials. Cabinet members were not given details of those trims in yesterday's meeting, but officials said specifics will be sent to them shortly by Stockman's OMB.

Yesterday's session was designed to give Cabinet members an overview of the budget and "soften them up for later," said one official. "It was designed to let them know that next time you show up . . . don't come in here with all your sacred cows."

Stockman painted a "grim picture" of the deficit that the administration must tackle, said another official. A third administration source said Stockman gave the Cabinet a "very much unvarnished" look at the fiscal problem.

In Reagan's economic blueprint of February 1981, the federal budget was supposed to swing into balance by fiscal year 1984.

In his presentation yesterday, Stockman was said to be working on the assumption of a modest economic recovery, with unemployment declining somewhat and interest rates falling below double digits in the fiscal year beginning next Oct. 1.

The new deficit projections -- which assume no budget cuts or tax increases -- are much larger than the $92.6 billion estimated for 1984 by the administration last July in its midyear review of the economy. They are also considerably more than the $152 billion estimated in September by the Congressional Budget Office.

The projections do not include $15 billion to $17 billion a year in so-called off-budget items that also add to the federal debt, an administration official said.

Sources said Stockman's presentation, made earlier in an expanded form to the president, was generally accepted by the Cabinet members. "There was not a lot of grimacing," said another administration official. "They are all pretty dedicated to bringing the deficit down.

"They were told there is a serious deficit problem -- and that pretty much frames the argument," this official added.

Treasury Secretary Donald T. Regan was reported to have argued part of the deficit was "cyclical," or related to the recession, and part was "structural," or built in by policy. Sources said Regan argued that the size of the deficit was "fluid" and could shrink if the economy picks up.

Richard S. Schweiker, secretary of health and human services, was reported to have asked the president to hold several more such sessions to involve the Cabinet in the decisions Reagan makes on the budget. Schweiker was reported to be concerned that the Cabinet not be left out of the overall budget deliberations because they will be asked to defend the package later.

The rising deficit projections underscore the budget dilemma facing Reagan. The recession and declining inflation have eaten away at government receipts while placing new demands on federal spending for social programs.

Reagan said in a speech in New Orleans this week that he was determined to bridge the budget gap by making more cuts in non-defense spending. He refused to budge on his build-up in military spending and insisted on proceeding with the third installment of his income tax cut and the scheduled 1985 indexing of tax rates to inflation.

But the new deficit projections suggest it won't be easy for the president to reduce the deficit to around $100 billion.

Reagan has already ruled out major reductions in projected defense spending. It also is still uncertain what will be required to put Social Security back on a sound financial base. When these two categories of government spending are combined with interest payments on the federal debt, they comprise about two-thirds of projected 1984 outlays.

To reduce the deficit by $80 billion without raising taxes, Reagan would have to trim that amount from the remaining third of federal spending. This would require deep cuts in domestic programs at a time when Republican congressional leaders and state governors are telling the president there is no more room for such cuts.

The White House also is still debating what tax policy Reagan should pursue next year. Treasury Secretary Regan has suggested advancing the last installment of the across-the-board personal income tax cut to stimulate economic growth. But the move is opposed by other administration officials, including Martin Feldstein, chairman of the president's Council of Economic Advisers, and Republican leaders have said that Congress is unlikely to approve it.

White House spokesman Larry Speakes said yesterday that the idea remains under "serious consideration" despite objections from Republican congressional leaders. Another administration official said that the president now seems to be "leaning toward" it.

The president made consistency one of his chief arguments for the tax cut in 1981, but already this year he has backed a tax increase and is now considering another shift in his original schedule for the three-part, 25 percent across-the-board cut.

Yesterday, in a satellite television broadcast sponsored by the U.S. Chamber of Commerce, the president said the current 10.4 percent unemployment rate is "unacceptable" and added that the administration's "most urgent priority is to see that we have enough jobs for all the people who want to work."

"Recovery will come gradually because we're determined not to repeat the quick-fix mistakes of the past," he added.