Without new spending cuts or tax increases, the federal budget deficit will hit $109 billion this year, $152 billion in 1983 and $162 billion in 1984, according to the Reagan administration's latest internal estimates.

These figures, which are sure to intensify the forthcoming fights over budget cuts for fiscal 1983, are far higher than previous estimates by the administration but in line with predictions of several private economic forecasters.

Deputy White House press secretary Larry Speakes yesterday called the new numbers merely "working assumptions at a staff level" and "highly preliminary," saying they had not been presented to the president.

But other sources said President Reagan was given the new bad news from his economic and budget advisers last Friday.

Reagan was said to have resisted any suggestion that he try to reduce the projected deficits by not increasing defense spending as much as planned or by proposing major tax increases. Instead, the president again indicated he wants further spending cuts in non-defense programs other than Social Security, sources said.

A White House official said he does not expect Reagan to reverse himself on this. The military buildup remains the president's first priority and stimulating economic activity through tax cuts intended to increase private incentives is the second, the official said. Reducing the deficit takes a back seat to these goals, he indicated. Reagan has already acknowledged that he will not redeem his campaign promise of a balanced budget by fiscal 1984.

Less than three months ago Reagan urged Congress to approve $16 billion worth of additional spending cuts and tax increases in order to reduce the prospective 1982 deficit from an estimated $59 billion to $43 billion. In what may be a sign of the budget-cutting troubles to come, he has now retreated and agreed to accept only about $4 billion of these deficit-reducing actions.

The 1982 deficit estimate has risen mainly, however, not from any congressional recalcitrance but because the economy has dropped so swiftly into recession. Reagan's advisers told him they expect the recession to end by spring, but only after the economy drops at about a 5 percent annual rate this quarter and a 0.5 percent rate in the first quarter of 1982.

By the third quarter of next year, the economy is expected to be bouncing back strongly, with real output rising at more than a 5 percent rate--a recovery that is supposed to continue unabated through 1983 and 1984, under this new scenario.

One administration economist, however, cautioned that the recession could be somewhat deeper and last somewhat longer than allowed for in the new estimates. Moreover, he said, the looked-for growth rate of more than 5 percent in 1983 and 1984 is "not a forecast but a policy target."

Inflation, meanwhile, is supposed to abate, with the gross national product deflator, the broadest of inflation indices, rising 7.7 percent in 1982, 5.5 percent in 1983 and 4.4 percent in 1984.

Unemployment, 8.4 percent in November, will rise above 9 percent before declining, according to the forecast. Nine percent is the post-World War II record.

Economists generally believe a deficit in the $100 billion range can be financed in 1982 without a surge in interest rates, because the recession is cutting deeply into private credit demand. But if the deficits persist at such a level once the recovery is under way--and the Federal Reserve continues to restrict growth of the money supply to hold down inflation--interest rates could climb above their previous highs, the economists warned.

Administration officials were upset that their detailed forecast had been leaked to the press.

"These are internal planning numbers," declared Lawrence Kudlow, chief economist of the Office of Management and Budget. "They are unadjusted, unscrubbed and have virtually no meaning in their present form. It's a shame the numbers got out."

Kudlow said the numbers are misleading because they include no allowance for any policy recommendations Reagan may make in January. Kudlow declined to discuss the forecast itself.

There will be little Reagan can recommend that would change the 1982 budget outlook substantially.

All along, the administration has assumed there would be further non-defense spending cuts for 1983 and 1984. In fact, some were proposed in September, along with a few minor tax increases. The significance of the new administration figures for the later years is the magnitude of the cuts that would have to be made in a recession and election year to reduce the deficit to manageable size.

Not only Congress is likely to resist deep further cuts. Even within the administration, Cabinet officers this week are appealing slashes in their 1983 budgets ordered up by OMB. The new estimates could strengthen OMB's hand in resisting these appeals.