The price of SALT II is sharping up as an extra $8 billion a year for defense that no one in Congress or the Carter White House has yet figured out how to spend.

It could prove to be an impossible task.

Sen. Sam Nunn (D-Ga.), the Joint Chiefs of Staff and Henry A. Kissinger are among those who have said they can support the strategic arms limitation treaty only if defense spending keeps climbing. Nad the White House is willing to go along, at least part way.

But Nunn is calling for increasing the Pentagon budget by 5 percent a year for the next five years, after allowing for inflation. That would mean a record $216.6 billion in defense spending by fiscal 1984.

The White House has agreed at this point to propose spending levels that would provide real growth of 3 percent a year.

"This is a fun business," chuckled one Pentagon executive, conceding that he did not know how the extra $8 billion a year Nunn wants would be spent.

"I don't know what they'd buy," added one White House budget official when asked how an extra 5 percent could be laid out profitably for strategic weapons such as missiles, bombers and submarines.

Nunn, while writing President Carter yesterday that "real increases of at least 4 to 5 percent in the overall budget are essential," has not drawn up any detailed list of where the money should go.

He said yesterday in an interview that it would be September before he could say specifically which defense programs should be increased.

But his letter, which also was signed by Sens. John G. Tower (R-Tex.) and Henry M. Jackson (D-Wash.), called on Carter to "make public your intentions" for the next five years of defense budgets. Nunn and Jackson are majority members of the Senate Armed Services Committee, and Tower is the ranking minority member.

This, however, may turn into an Alphonso and Gaston act, since it was learned from White House sources yesterday that the president plans to call in Nunn and other senators to ask them what programs they believe need additional money.

The White House also wants to know just how widespread within the Senate and the House the desire to increase defense spending really is.

Within the community of defense spending specialists there was wide disagreement on the impact of the 5 percent spending increase proposed by Nunn. The $8 billion-a-year estimate comes from the Office of Management and Budget Committee, however, estimated the boost in pentagon spending at $20 billion a year.

Chairman Joseph P. Addabbo (1)-n.y.) of the House defense appropiations subcommittee said in an interview that the Pentagon already has $20 billion in congressionally appropriated funds backed up in its spending pipeline.

"We've already got a complete arenal of missiles: we're putting billions in the MX; shipyards are already that are fully funded," Addabbo said. "I don't know what you would do with that much extra money. Dollars don't buy national defense."

Carter asked White House budget chief James T. Mcintyre Tuesday if an extra 5 percent a year could be spent profitably by the Pentagon. Sources said Mcintyre's opinion is that no vital military programs are going begging either in the fiscal 1980 budget before Congress or the fiscal 181 budget in preparation.

The White House guidance to Pentagon budget chiefs so far is to stick with last year's goal of increasing military spending by 3 percent a year after allowing for inflation.

Administration officials have conceded that rising inflation has already wiped out about the half fiscal 1980 growth and may require a supplemental request of $2 billion to restore the percent increase.

One hint as to where Nunn would put more money came in the letter to Carter, which singled out "the crucial areas of real military investment in weapons, ships, equipment and research and development" where the Soviet "have been outspending the United States by 2 to 1. . . ."

A White House budget official said yesterday that he would be hard pressed to come up with projects to match the money being proposed.

One prospective program, adding an additional Trident strategic nuclear submarine each year, could absorb the funds, "but we don't have shipyard capability to build more than one," he said.

Another program area, building modern medium-range nuclear missiles for the European theater "could be pushed full speed ahead," he said, but political problems in basing the weapons have been the main holdup on development and procurement.

During a colloquy with Gen. Richard Ellis, commander of the Strategic Air Command, at yesterday's Senate Armed Services SALT II hearings, Nunn zeroed in on another area for increase: modernization of the B52s.

Nunn questioned Ellis about Defense Secretary Harold Brown's eralier statement to the committee that, by 1985, 75 percent of the B52s sent to attack the Soviet Union would reach their targets.

Ellis confirmed the testimony, but conceded to Nunn that Brown had not yet funded all the B52 upgrading programs that would enable that many of the aged, long-range bombers to penetrate Soviet air defenses.

"His [Brown's] projection was based on some unfunded programs?" Nunn asked. Ellis agreed.

Later Nunn told a reporter that his concern "was for a steady spending program" and a presidential commitment to support it.

He pointed out that President Carter's pledge of a 3 percent spending increase, made to the NATO countries, "is not being kept," and cited how it had been allowed to fall under House Budget Committee cuts.

"There was no White House fight on the House side against those cuts, I've been told by some members," Nunn said.

But when asked yesterday where the additional billions for the defense program would come from, Nunn stared straight ahead and did not answer.