Budget Director David A. Stockman told President Reagan and the Cabinet yesterday that the budget news for the current year is worse than Stockman believed a week ago, but the president said he is determined not to propose a tax increase or "submit a budget that would cause us to acquiesce in a tax increase," administration sources said.

Stockman, whose estimate late last week was that the deficit would be in the $190 billion range in the fiscal year that began Oct. 1, told the president and the Cabinet that new figures suggest that the red ink is headed for $210 billion.

Administration sources said Stockman also said federal spending this fiscal year will reach 24.5 percent of gross national product. That would be a slight increase from last year, when it was 23.5 percent, though down from fiscal 1983, when the government consumed 25 percent of GNP, largely because of the recession.

Reagan was described as "taken aback" by the new estimates from his budget director, who has been accused in the past by anti-tax supply-side theorists of exaggerating his deficit forecasts to pressure the president into a tax increase.

But in yesterday's start of the budget jockeying expected to continue for months, Reagan reportedly said, "I will not submit a budget with a tax increase" or a budget that would encourage others to think he might acquiesce in one.

Sources also said that Reagan took from his pocket a copy of a 1964 speech he delivered on national television for Republican presidential nominee Barry Goldwater, entitled "A Time for Choosing," and read portions of it to the Cabinet. That speech, which launched Reagan's political career, called for reducing the size and scope of government.

"This is what we came here to do," one source quoted Reagan as telling his aides.

Stockman told the Cabinet that deficit estimates that he has worked on in recent days show that the fiscal 1985 deficit, which in August the administration had said would be about $175 billion, will likely reach $210 billion, and $223 billion if off-budget items -- mostly federal credit programs -- are included.

Officials said the Stockman estimate rose over the weekend in part because of new figures on spending approved by Congress just before adjournment, plus new figures on the impact of the slowing of the economy in the third quarter.

Reagan said frequently in his reelection campaign that economic growth would reduce the deficit, because expansion increases revenues and cuts some government costs.

The ideas that growth can bring down deficits without a tax increase and that a tax increase would impede growth are important articles of faith among supply-siders. But Stockman's report to the Cabinet indicated that growth is not having that effect currently and that, instead, the deficit is increasing even in a time of economic expansion.

Reagan has also talked about reducing the growth of government to about 5 percent per year. But Stockman reportedly told the Cabinet yesterday that while government spending increased 5.8 percent last fiscal year, it is rising at a rate of 13.5 percent this year and is expected to rise 7 percent in fiscal 1986.

All the estimates are current-services figures, meaning they are projections of revenues, spending and the deficit under existing policy and law. Reagan is expected to seek deep new spending cuts in January.

One official familiar with yesterday's meeting said Stockman's message was that the "premise of the campaign," that deficits would melt away with economic growth, "was not being validated."

The official said there were several reasons why fiscal 1985 appeared to be turning out worse than fiscal 1984. He said unemployment-insurance costs have been rising, as have costs in Medicare and Medicaid. Also, the Defense Department is spending money faster this year, and farm support costs fell in 1984 in a drop not expected to be repeated this year.

Reagan promised in the campaign that he would not raise taxes and attacked Democratic nominee Walter F. Mondale for saying an increase was necessary. Some aides had theorized, however, that after the election Reagan would let Congress raise taxes for him, over his objections, as he did in his first term. Yesterday's reported comment seemed to shut the door for now on such a ploy, however.

Sources said the Stockman estimates are predicated on 4 percent annual economic growth and declining interest rates, inflation and unemployment.

Reagan's top advisers are said to be split about how to deal with the deficit this year. Some, including White House counselor Edwin Meese III, reportedly have advocated reducing it entirely through spending cuts and economic growth. Others have expressed skepticism about whether Congress would accept such cuts, since Reagan has put defense spending and tax increases off-limits.