The Carter administration yesterday went all the way back to Alexander Hamilton in an attempt to take some of the political sting out of President Carter's veto of the $37 billion defense bill.

Defense Secretary Harold Brown wrote Chairman Melvin Price (D-Ill.) of the House Armed Services Committee that the president, in his veto message, was not trying to "question the vital role of the Congress in the legislative process" or claim superior knowledge.

Instead, said Brown, Carter was exercising his veto power in the spirit of Hamilton, who wrote that "the propriety of the thing does not turn upon the supposition of superior wisdom or virtue in the executive, but upon the supposition that legislature will not be infallible . . ."

Brown's letter to Price yesterday followed one the president sent to the committee on Friday assuring Price "of my awareness of the positive and constructive constitutional role of Congress in providing for our nation's defense . . ."

Price has protested to Carter a day earlier that his veto message sounded as if the president considered Congress a poor relation rather than a full partner in making national defense policy.

The administration's campaign to soothe the feelings of Price, Sen. John C. Stennis (D-Miss.) and other congressional defense leaders has failed to head off the mobilization of anti-veto forces by House hawks.

The attempt in the House to override the veto is scheduled for tomorrow. If it is sustained, the Armed Services Committee will rewrite the bill - taking out the $2 billion authorized for the nuclear aircraft carrier that Carter does not consider worth building.

Rep. Charles F. Bennett (D-Fla.), chairman of the House seapower subcommittee that championed the carrier, yesterday held "my first news conference in over 30 years of public life" to protest the veto.

The president's veto message, Bennett said, contained "many, many factual errors" because Carter "was just horribly misinformed." Bennett said the conventionally powered, large carrier the president has pledged to put in his defense budget next year would end up costing more than another nuclear carrier of the Nimitz class because it "would amount to a custom-made ship."

This morning, two hawkish House members - Samuel S. Stratton (D-N.Y.) and Jack Kemp (R-N.Y.) - are scheduled to hold a breakfast as part of their effort to drum up support for a veto override.

House Speaker Thomas P. (Tip) O'Neill Jr. (D-Mass.) has said he believes tomorrow's override attempt will fail. A two-thirds vote is required.

Brown, in yesterday's letter to Price, said "the issue is a simple and narrow one: it is whether the defense of the United States is enhanced more by allocating $2 billion of limited defense dollars to buy a nuclear-powered aircraft carrier in fiscal 1979 or whether, instead, that money should be spent on other defense needs which the president and his defense advisers believe are more pressing, and which were included in the budget request which the president submitted with my concurrence and with that of the joint chiefs of staff . . ."

Brown noted that "sincere and reasonable persons can differ" on that question, pointedly reminding Price that Congress "only last year" voted to delete money for the very same $2 billion Nimitz-class carrier that caused Carter to veto this year's defense authorization bill.

"I hope that you will accept the president's disapproval as an expression of his and my strong conclusion that the carrier is not the proper use of our defense funds in fiscal year 1979," Brown wrote.

Assuming the president's veto is sustained and the House rewrites the defense bill, the Pentagon has drawn up a list of project it would like added.

Under money authorized to buy military hardware - the procurement account - the Pentagon requested $247.5 million be added, with the biggest single addition being $40 million to modify civilian aircraft so they could carry war cargo in an emergency.

An additional $209.5 million was requested to restore cuts in research programs, including $30 million in across-the-board cuts in advanced Navy and Air Force technology.

The Pentagon said a total of $457 million was considered high-priority candidates for restoration. It figured with the $1.930 billion in Nimitz money deleted, the total money authorized for weapons and research in fiscal 1979 would be $35 billion.

A White House official said yesterday that Carter realized at the time he vetoed the authorization bill that some of the congressional actions he objected to in his message were actually done by the appropriations legislative process.

However, he said, the two processes are connected and determine how the defense dollar is ultimately apportioned. The White House executive, who did not wish to be identified, said Carter felt he owed it to Congress to register his objection as soon as possible by vetoing the bill on his desk, the authorization bill, rather than waiting for the appropriations bill still making its way through Congress.