President Reagan, bowing to the growing budget deficit and strong opposition on Capitol Hill, yesterday dropped the idea of moving up from July to January next year's scheduled 10 percent cut in income taxes.

The president, flanked by Senate Majority Leader Howard H. Baker Jr. (R-Tenn.) and House Minority Leader Robert H. Michel (R-Ill.), said he will not push to accelerate the tax cut because such a step would increase the deficit, lacks support in Congress and could boomerang if Democrats tampered with the cut instead of just speeding it up.

It was the second time this week that the president alluded to the enormous deficits he faces.

On Monday in Los Angeles, he said the budget can no longer be balanced by spending cuts, as he used to assert, but requires a recovering economy. And new projections prepared by David A. Stockman, director of the Office of Management and Budget, show that even with the recovery anticipated by the administration, the likely deficits will remain in the $200 billion range through the late 1980s.

In addition to giving up on the tax cut speedup, Reagan also vowed yesterday to keep resisting Democratic proposals for public works programs to stimulate the economy. But House Speaker Thomas P. (Tip) O'Neill Jr. (D-Mass.) said Democrats would try to attach their latest such $5 billion proposal to the continuing resolution Congress must pass by Dec. 17 to keep most government agencies in funds. This could set up a veto confrontation that could shut the government down temporarily at Christmastime. Details on Page A6.

The president has come out, however, for one new program--a 5-cent-per-gallon increase in the gasoline tax to finance a highway and bridge repair program. He reaffirmed his support for it yesterday and the Senate Finance Committee began hearings on it; it has bipartisan backing and is expected to sail through the lame-duck session of Congress this month. Details on Page D9.

Before leaving for his Latin American tour yesterday, the president met with 23 Republican congressional leaders on the tax cut and his agenda for the lame-duck session.

Speaking afterward to reporters in the White House briefing room, Reagan said his priorities for the session are the highway tax and repair bill and his enterprise zone legislation.

The president also handed the congressional leaders a full plate of other issues on which he wants action.

They include his Caribbean Basin initiative; money for the MX missile; revisions in the Clean Air Act; nuclear waste disposal legislation; a revision of federal bankruptcy laws; regulatory reform; immigration reform; the Radio Marti proposal; and the anti-crime bill already approved by the Senate.

When asked what chance Reagan has of winning this secondary agenda, Baker would only reply laconically: "Some chance."

But the one item that had most concerned the congressional leadership in both parties was disposed of in the meeting yesterday. Last month, Reagan raised the possibility of advancing the final installment of his three-year tax cut from July to January, describing it as an "appealing" way to stimulate the stalled economy.

But White House officials said that Reagan had doubts about the idea over the weekend. They said he finally made up his mind after a "spirited" talk with Republicans yesterday.

His decision was influenced, they said, by a memo over the weekend from Treasury Secretary Donald T. Regan, who had originally pushed for advancement of the tax cut but for various reasons reversed himself.

But Reagan seemed reluctant to let go of the tax cut acceleration. He said in a prepared statement that "there continues to be interest in the possibility." Only when asked by reporters did Reagan admit he was dropping it.

The president's doubts about accelerating the tax cut were fueled by telephone conversations Reagan had from his California ranch over the weekend with Republicans on the tax-writing committees in Congress, officials said. Baker and Michel, as well as other members of Congress, had told Reagan he lacked the votes for the tax cut acceleration.

In addition, Reagan was cautioned that by asking Congress to speed up the tax cut now, he might open it up to tampering by Democrats. Questioned why he had backed off from the idea of a tax cut acceleration, the first reason offered by the president was "what opening that whole subject up might do."

"We think the most important thing is to resist efforts that probably will be made to go the other way," Reagan said of the tax cut. "We discussed the difficulty of getting this passed because, as I say, there are elements up there who want to go the other way, which I think would be directly opposed to what is needed today if we're to restore the economy, would be to go the other way and take away that incentive."

Another reason the president offered for scrapping the idea was concern over deficits. While the tax cut acceleration would stimulate the economy, Reagan said, "It's a stimulant that actually occurs down the line a little ways, and the first result in this time of high deficit would be an addition to the deficit."

Baker, who opposed the tax cut acceleration, left the meeting with the president in high spirits, saying it was the "freest exchange" he's ever had with Reagan. "He changed his mind. I admire him. He said he came to ask and listen, and he did listen."

Questioned whether Reagan's decision signals a more accommodative outlook, Baker said, "I don't sense that there is any difference in the president's general attitude." While Reagan may modify his program "to the extent . . . that current circumstances would indicate he should," Baker added, "I see no willingness to abandon any of the major aspects of that program or to compromise for the sake of compromise."

Michel, asked to predict the outcome of a House fight over funding for the MX missile, said that Thursday will be a "very critical day" when it comes to a vote in the House Appropriations Committee. " . . . If it fails in the committee that's obviously going to make it all that much more difficult to carry on the House. . . it's going to be touch and go."