Advocates of increased defense spending pressed President Carter yesterday to boost his fiscal 1981 Pentagon budget beyond the already hefty jump he has proposed, and there were indications they may get their way in Congress.

Sen. Jake Garn (R-Utah) said he and his colleagues told the president at a White House breakfast for Republican legislators yesterday that his fiscal 1981 budget was "very inadequate and totally unrealistic."

Later, in an appearance before the Senate Armed Services Committee, Defense Secretary Harold Brown faced a repeat of Tuesday's hostile questioning before the House Armed Services Committee.

Sens. Harry F. Byrd (Ind.-Va.) and Henry M. Jackson (D-Wash.) zeroed in on whether Carter could make good on his pledge to protect vital oil supplies in the Persian Gulf.

"We can't assure you we could win a war there," Brown said. "But to cast doubt on our abilitity to deter or fight effectively is . . . unnecessarily damaging to U.S. security.

"The commitment is to fight. It would be a mistake to assume a war between the United States and the Soviet Union can be won by either side."

Jackson asked whether Carter had any commitments from Persian Gulf countries that they would help the United States resist Soviet actions in that oil-rich region. Brown responded that the United States had "indications" it would be able to use ports and airfields in the area.

This skepticism about the adequacy of Carter's defense budget and his commitment to defend the Persian Gulf is building pressure in Congress to blow the lid off his proposed fiscal 1981 Pentagon budget.

Carter proposes to let the Pentagon obligate $158.7 billion, a 14 percent jump over the fiscal 1980 total, which the Pentagon figures as a 5.4 percent increase, allowing for inflation.

Chairman Edmund S. Muskie of the Senate Budget Committee said he had fought hard, but unsuccessfully, against the attempt to raise budget ceilings to allow defense spending to rise 3 percent in fiscal 1980 and 5 percent in fiscal 1981 and 1982.

Muskie said he expects to resist efforts to add money to the new Carter defense budget, declaring: "I don't think we ought to trigger a splurge of spending."

With a smile, Muskie noted he lost that same uphill fight last year and said, "I think that this time the hill has grown a little steeper and a little craggier."

Sen. Strom Thurmond (S.C.), second-ranking Republican on the Armed Services Committee, said his party will fight for more than Carter's proposed 5.4 percent increase, predicting that the rise, after inflation, will come closer to 10 percent. Thurmond said he thought the increase should be 20 percent.

Sen. Gaylord Nelson (D-Wis.) said his survey of the political landscape leads him to believe that add-ons to the defense budget could come in one of two ways.

Either such Senate influentials as John Stennis (D-Miss.) and Sam Nunn (D-Ga.) will make the case for a higher budget, or Republicans will mobilize in both the Senate and the House to outdo Carter "and then pick up enough votes from our side to win," Nelson said.

Sen. William Proxmire (D-Wis.), a frequent critic of the Pentagon, said it was "absolute nonsense" to pretend that a single percentage figure could determine how much was enough for defending the United States. "Imagine how irresponsible they would call us if we did that for HEW," Proxmire said.

Even so, he continued, "it will be hard to hold back the tide this year."

Chairman Robert N. Giaimo (D-cOnn.) of the House Budget Committee agreed, blaming the pressure to increase defense spending on congressional anger and frustration over the Soviets' flexing of their military muscles.

"There are hawks," Giaimo said, "who will insist on building the B1 bomber and another Nimitz [nuclear] aircraft carrier" in response to the Soviet actions. But, he contended, this would be the wrong way to go because the real need is for weapons that can project American power in distant places such as the Persian Gulf. He cited ships for carrying Marines and more money to repair conventional weaponry.

"We have to make sure we're spending the money wisely," Giaimo said. He said the Soviet invasion of Afghanistan "doesn't make a case for the B1 bomber."

However, he predicted there will be a chance this year to make that link, as evidenced by the House Armed Services Committee hearing on Tuesday when several members said they would insist on bringing back the B1, which Carter canceled in favor of the cruise missile.

Asked if the White House would go along with Congress if it adds money to Carter's proposed defense budget one administration aide vowed that "this will be resisted."

Both Brown and Air Force Gen. David C. Jones, chairman of the Joint Chiefs of Staff, stressed yesterday that what was needed to build up U.S. defenses was a steady, sustained growth in military spending, not a roller-coaster ride of funding.

Asked after the hearing if the joint chiefs would go along with a 10 percent real increase instead of the 5.4 percent one proposed by Carter, Jones said the extra money could be well spent but he would not want to come out in favor of such an increase unless he knew whether it was to be sustained in future years or would be a one-time hike.