The House of Representatives left town Friday. The Senate will do the same shortly. President Carter is off on a raft somewhere in Idaho. But inside the White House, presidential aids, remain preoccupied with a legislative issue - Carter's veto last week of a $36 million weapons precurement bill.

On Sept. 7, two days after returning from its recess, the House will take up the veto in a vote that could set the tone of relations between the White House and Capitol Hill for the rapidly dwindling days left to the 95th Congress.

The president announced the veto last Thursday during a nationally televised news conference. He objected most strongly to the inclusion in the bill of $2 billion for a new nuclear aircraft carrier, which he characterized as two costly and vulnerable. He also argued that to pay for the carrier, the Congress was refusing to fund other, more important military programs.

The White House, recognizing the stakes involved for Carter, is mounting one of its most concerted efforts to date to sustain the veto.

A special task force, headed by Vice President Mondale's chief of staff, Richard Moe, is now meeting daily to coordinate the effort. Mondale, national security affairs adviser Zbing niew Brzezinski, both of whom strongly favored the veto, and Defense Secretary Harold Brown, who reportedly had mixed feelings about it, are expected to play the leading roles in selling the administration's case.

This afternoon, as part of the effort, about 150 business and civic leaders from around the country will be welcomed to the glitter of the East. Room of the White House to hear a pitch from Mondale and others, and - administration officials hope - return home as advocates of the president's position.

One official compared the effort being made to sustain the veto in everything but scope to the White House's year-long campaign to win approval of the Panama Canal treaties, in which such briefings for civic groups played a major role.

There are other similarities to the Panama votes, particularly in the political stakes involved for the president. When the Senate approved the canal treaties, it was widely interpreted - and never seriously disputed in the White House - that it was less a great victory for Carter than the avoidance of a potentially debilitating defeat.

It is much the same with the weapons authorization veto. If Carter prevails, as his aides believes he will, it is not likely to tranform overnight the image of inept congressional relations that surrounds the administration.

But should he fail to convince a Democratic Congress to sustain him on the first important veto of his 19-month-old administration, Carter's image as a president who has never gained control of the government would deepen. And that in turn could affect how the Congress treats the administration in the few weeks between now and the fall elections as it takes up such matters as natural gas legislation, the tax reduction bill and the civil service "reform" legislation.

It was because of such factors that the president's political advisers were the most hesitant about the veto. They worried about the chances of sustaining the veto and that a highly visible defeat on the issue would all but doom Carter's hopes of getting some of the administration's other major pieces of legislation through Congress this year.

But the president, according to his aides, brushed aside these arguments, a decision that has cheered numerous officials who believe Carter's so-called new "toughness" is more than image, that he is finally "following his own instincts" and will reap dividends in the long run.

In the veto of the defense measure, and in his accompanying threat to veto other legislation, Carter appears to have reached a turning point in his relations with Congress.