Senate Republican leaders decided yesterday to go ahead today on President Reagan's budget for next year, after toying with the idea of a delay to give the administration time to fend off likely cuts in its big proposed increase in defense spending.

The day of behind-the-scenes maneuvering followed a meeting late Monday at the White House during which Reagan joined Defense Secretary Caspar W. Weinberger in insisting on their defense spending proposal over objections from Senate Budget Committee Chairman Pete V. Domenici (R-N.M.) and others that the GOP-controlled Senate won't buy it.

It was a "very, very tough meeting," said an aide to one of the participants.

According to aides, Domenici told the president that the Budget Committee may not be able to draft a budget with more than a 5 percent increase for defense after inflation, which is only half of what the administration has proposed in its $245.3 billion spending proposal for the Pentagon next year.

"I don't see how we're going to get a budget under the present circumstances," Domenici told reporters yesterday.

The difficulty of getting agreement on the committee, coupled with administration plans to step up its campaign to win public support for Reagan's military buildup, gave rise to suggestions at the Monday afternoon meeting for a week's delay in committee work on the budget. It was scheduled about a month ago to begin today.

While neither Reagan nor Weinberger made a formal request for a delay, there was disagreement over where the idea originated.

Early reports by staff members of senators who participated in the meeting that the idea originated in the White House were quickly denied by Senate Majority Leader Howard H. Baker Jr. (R-Tenn.), who told reporters that a delay was his suggestion.

"We've got a first-class flap . . . and I would like to see us not face the issue until we've worked it out," said Baker, who earlier had been urging quick action on the budget.

An administration official agreed that it was Baker's idea but added, in reference to Reagan and Weinberger, "they did not discourage him."

Others said privately that the White House wanted the delay to give it time to sell its case that the Soviet military threat is greater than generally believed. The possibility of a nationwide television address on the subject was discussed at the Monday meeting and embraced by Senate Armed Services Committee Chairman John G. Tower (R-Tex.), sources said.

Reagan was as adamant as Weinberger in insisting on the administration's defense spending proposal, several sources said. Both, said Baker, were "pretty adamant."

"The administration's response to suggestions of defense spending cuts was not just no, hell no, but that the Russians are already in Chicago and about to take Peoria," said one congressional aide familiar with the administration's arguments.

By late afternoon, Baker abandoned the idea of a delay in a private meeting with Domenici, who reportedly was not enthusiastic about delaying his committee's work, which he had hoped to complete by the middle of next week.

An aide to Baker said the majority leader did not ask Domenici to postpone today's opening session of the budget markup, although other sources said it may well be next week, at the earliest, before there is a showdown on defense. This would give the administration at least some time to lobby for its budget request.

No more than three committee members now are believed to support the administration's proposal to raise defense outlays from $214.8 billion to $245.3 billion, an increase of more than 14 percent before inflation and about 10 percent after accounting for inflation.

Several members said yesterday that a majority of the committee probably would settle for a 5 percent increase, although the committee may vote for 6 or 7 percent as a bargaining position for a budget conference with the House, which is considered likely to approve a smaller figure.

"I think there's a pretty broad feeling that 5 percent is about right," said Sen. Slade Gorton (R-Wash.).

"I believe the Budget Committee, if it could settle right now, would settle at 5 percent real growth," said Sen. J. Bennett Johnston (D-La.).