The Pentagon's budget, which in fiscal 1982 is already at a record level, is likely to run as much as $10 billion over projections for the next fiscal year, threatening President Reagan's whole economic program, including his pledge to balance the federal budget by 1984.

Deputy Defense Secretary Frank C. Carlucci acknowledged in an interview that the administration's rewrite of President Carter's final two military budgets is running $2 billion to $10 billion more than had been anticipated in bills coming due in 1983.

The overrun would make it more difficult for the administration to meet its spending targets in future years. Congress has cut nearly $40 billion in spending from the 1982 budget, and, according to admnistration figures, will need to cut at least $30 billion more from the 1983 budget and $44 billion from the 1984 budget if it is to be balanced.

Those figures do not reflect the higher-than-anticipated defense spending, which a secret internal Pentagon memo puts at $6 billion. The memo warns that Reagan must either raise the ceiling for military spending further or do without some of the weapons he just finished ordering.

The record high peacetime budget of $222 billion for fiscal 1982 will have to be raised by 9 percent after allowing for inflation, rather than the 7 percent planned, to accommodate the huge increases, the Pentagon memo said.

"Even the planned 7 percent growth in fiscal 1983 through 1987 does not permit the services to implement all the programs planned earlier," the memo said. It cited Reagan's decisions to build a new bomber, raise military pay and construct more ships as examples of initiatives adding about $38 billion to the fiscal 1983 defense budget.

"The situation will only be exacerbated, and the shortfall continued further into the out-years if real inflation is different from that otherwise assumed," continued the bad news memo, which was circulated between the Pentagon's E ring and the White House Office of Management and Budget.

"There is a substantial tail on the 1982 programs which is going to complicate our life in the out-years: 1983, 1984 and 1985," Carlucci acknowledged during the interview Friday in his third-floor Pentagon office. He said the extra cost could amount to somewhere between $2 billion and $10 billion for fiscal 1983.

"We knew this when we were putting the programs together," he said. "But the issue of whether we can live within the 7 percent guidance is something I can't speak to until I've looked at the program proposals and see what the tradeoffs are and establish priorities."

By program proposals, Carlucci meant the budget requests the miltary services are putting together now. Final Pentagon judgments on the requests are expected late next month.

Although he declined to discuss rumors rocketing around the Pentagon that Defense Secretary Caspar W. Weinberger already has asked Reagan to go beyond 7 percent real growth in annual Pentagon budgets, Carlucci said that "We have been talking in broad terms with OMB on the dimensions of the problem."

Asked if Reagan had been briefed on the bulge building in next year's budget, Carlucci would not go beyond saying that "certainly decision-makers on the other side of the river are aware of the dimensions of the problem."

It is too early in the budget process for the White House to change its guidance to limit annual increases in the amount of money the Pentagon can obligate, but not necessarily spend in one year, to 7 percent for fiscal 1983 through 1987, Carlucci contended.

He said that by the end of August the Pentagon should know whether a 7 percent real increase over 1982 will be enough for 1983, given the big "tail."

Carlucci, who has done much of the backroom work in putting together Reagan's record peacetime military budgets and played a leading role in selling them to Congress, conceded that asking for more than the $254.8 billion in total obligational authority that the administration projected for fiscal 1983 is loaded with political peril.

He said Pentagon planners intend to make cuts to try to stay within the 7 percent guideline. "We're not exempt from the austerity regulations laid down by the president," Carlucci said. "We will be cutting programs."

However, he vowed to resist such false economics as buying new airplanes but not enough spare parts to keep them flying or stretching out purchases to the point that the savings of mass production are lost. He said that is what happened during the previous administration.

Asked whether he believed the 7 percent increase would be enough, Carlucci reflected for a moment and said quietly: "It's going to be a real challenge."

At the same time, he conceded that raising the defense budget higher than projected in fiscal 1983 would imperil the nation's always fragile pro-defense consensus. The risk will be especially high next year, he added, because the pain from this year's domestic budget cuts will have been felt by then.

"It is clear to us that in order to maintain the consensus in favor of a strong defense, a consensus which we think we have, it is going to be most important for those on the management side in the Pentagon to demonstrate greater efficiencies, that we're getting maximum value for the taxpayer's dollar," Carlucci said.

He stressed that the only way to correct what the administration regards as the adverse military balance with the Soviet Union is to keep increasing the U.S. defense budget year after year, not go up and down as in the past.

Other administration executives are zeroing in on the defense budget as they look for new places to cut the federal budget so it can be balanced by fiscal 1984, as Reagan has promised.

The $40 billion slash in fiscal 1982 programs was done without touching defense. Many officials say they believe this immunity must be lifted, given the political and economic realities.

The political storm kicked up when the Reaganites targeted Social Security indicates to a growing number of administration officials looking for cuts that defense is the new field to conquer.