President Reagan and leading congressional Republicans continued their complicated search for agreement on a new round of budget cuts and possible tax increases yesterday, and the White House sought to rebut what it called "an 'economic program in disarray' trend in the media."

A White House spokesman said such stories are not fair.

But there remained obvious differences within the party over how to reduce the projected deficits for this fiscal year, fiscal 1983 and fiscal 1984, when the president has vowed to balance the budget.

Republicans on the Senate Budget Committee were considering a proposal for at least $180 billion in unspecified spending cuts and tax increases over the next three years, of which $80 billion would come on the tax side.

But that is a much larger tax increase than the president has proposed--it would obviate about a fourth of the tax cut he pushed through Congress just three months ago--and House Minority Leader Robert H. Michel (R-Ill.) said after a meeting with Reagan yesterday, "There's no way you're going to get this president to be talking about a tax increase . . . . The president is very adamant that there be no tax increase, particularly in 1982."

Presidential spokesman David R. Gergen said, when asked if the president were flatly opposed to any tax increase, "I think that is stating the case too pointedly." He noted that Reagan himself has proposed about $22 billion in "revenue enhancement," or tax increases, over the next three years.

The current confusion began this fall when the White House added up the likely effects of the large tax and spending cuts Congress voted at the president's request in the summer. It found the spending cuts were not enough to get the deficit down to where the president wanted it. The president then said he would shortly send to Congress some $13 billion in further spending cuts plus $3 billion in revenue-raisers.

But congressional Republicans balked, and they have been arguing over alternatives ever since.

The president proposed in September that $2 billion be taken from the defense budget for fiscal 1982, about $3 billion from basic benefit or entitlement programs and $8 billion from domestic appropriations.

Congressional Republicans have generally been calling for larger defense cuts and tax increases than the president wants, and for smaller domestic cuts. Senate Majority Leader Howard H. Baker Jr. (R-Tenn.) has even suggested a temporary national sales tax as a revenue-raising possibility, and he and others have also suggested a windfall profits tax on natural gas if it is deregulated, as many Republicans and the gas industry want.

Gergen said yesterday the promised entitlement cuts are now in the final stages of review, under presidential counselor Edwin Meese III.

Reagan is supposed to meet with the Republican leadership of the Senate and the House sometime this week on the budget issue.

The Senate Budget Committee is now starting work on the second budget resolution for this fiscal year, setting spending ceilings and revenue floors which would be binding unless Congress expressly revoked them. It would be up to other legislative committees to vote the specific spending cuts and tax increases a budget resolution required.

The plan before the Budget Committee, which was circulated by Chairman Pete V. Domenici (R-N.M.), anticipates cuts over three years of $30 billion in defense and $25 billion to $30 billion in non-defense appropriations, according to committee sources. It also calls for cuts of $40 billion to $45 billion in entitlement programs, the sources said.

Together with an anticipated $9 billion reduction in interest costs, the total would add up to more than $180 billion, considerably more than the $115 billion that the administration recommended to balance the budget by 1984.

A committee source said that the proposal would lead to a balanced budget by 1984 based on assumptions that the committee is making about the economy's likely performance over the next three years.

Committee sources said the "general outlines" of the plan were discussed by Republican members of the committee yesterday and final action on it is expected today. The committee is scheduled to begin drafting a final budget resolution for fiscal 1982 on Thursday and, if the plan being circulated by Domenici is approved by the Republican majority, it is expected to be included in the resolution.

In further action on appropriations, meanwhile, the Senate rebuffed Reagan in approving a transportation money bill that exceeds his spending targets and voting to resume running a Washington-to-Chicago train that goes through the home state of Minority Leader Robert C. Byrd (D-W. Va.).

The bill, approved 77 to 15, orders resumption of service by the Cardinal, which was one of several trains ordered to halt service Oct. 1 because of budget cuts. The vote on the amendment to continue service by the Cardinal was 53 to 34.

The Senate also rejected, 52 to 39, a 4.1 percent across-the-board cut in transportation spending proposed by Sen. Mack Mattingly (R-Ga.). The proposal, the latest of several attempts by Mattingly to bring Senate money bills more in line with Reagan's spending targets, would have given Reagan about half the transportation cuts he wanted.

As the Senate was working its will on the transportation bill, Majority Leader Baker was saying he is exploring the idea of a special trust fund to finance the defense budget. But Baker denied well-confirmed reports from other sources that he was considering a national sales tax to finance the fund.

"I have not advocated, do not advocate and will not advocate a national sales tax," Baker told reporters. But he confirmed that there have been some discussions of it. He said others have suggested a sales tax, but he did not identify them.

Baker described the trust fund as "one of maybe 100 ideas running around the track" to finance Reagan's defense buildup without jeopardizing other programs or driving up deficits. Defense and domestic programs are vying for the same dollars, and "I am searching for ways to get them out of competition with each other," Baker said.

While insisting that he had ruled out a sales tax to finance the defense buildup, he said he was "not as adamantly" opposed to the idea of a value-added tax, which is a form of sales tax imposed on the value added to goods as they go through various forms of production. But he said he was generally opposed to the value-added tax as well.

Other sources said Baker had discussed privately with them both a sales tax and a value-added tax before reports of the discussions appeared Tuesday in The Washington Post and an Associated Press account. But the idea appeared to generate no discernible enthusiasm among Baker's fellow senators. "It died as soon as it left Howard Baker's lips," said a Republican colleague