President Reagan yesterday repeated, through a spokesman, that he opposes raising taxes next year, and reportedly also shot down some proposed spending cuts, including one to phase out the Head Start program.

His Office of Management and Budget, in one of a number of proposals to hold down the likely deficit in fiscal 1983, has urged that Head Start be merged into a broader block grant to the states and phased out as a separate program.

Reagan reportedly vetoed this, and also vetoed similar proposals by the OMB to phase out the present program of community development block grants and so-called urban development action grants to local governments.

In what has become almost a pattern in recent weeks, OMB Director David A. Stockman has been proposing huge cuts in programs, Reagan has agreed to only more modest cuts and the administration has in a sense been able to have it both ways: as economizer and savior of programs.

But the Stockman proposals illustrate the budget bind the administration is in as it prepares its spending plan for the 1983 fiscal year that will begin Oct. 1. It will send this to Congress early next year.

The administration's economists say they think the 1983 deficit will be slightly more than $150 billion without spending cuts and tax increases beyond those already provided by law. Congressional economists say they think the deficit could hit $175 billion.

Two reasons are the tax cuts Congress voted last summer at Reagan's behest and the defense spending increase he is pressing. Aides say he is backing off neither of these, and he said at his news conference last week that he had no plans for tax increases next year.

Even so, earlier this week there were reports that the president's senior advisers were urging him unanimously to back tax increases that could mount to over $40 billion over the next three years, as a way of trimming the deficit.

Yesterday, however, aides said no such proposal had been presented to him.

Moreover, White House communications chief David Gergen told reporters that, "The president, as he made clear last week, is opposed to any new increases in taxes. He believes that the growing burden of taxation has been a major contributor to the economic deterioration of recent years. He also believes that the tax cuts passed earlier this year lay a strong foundation for economic recovery in 1982 and should not be changed."

But Gergen left the door open for consideration of some kinds of tax increases, provided they do not interfere with the central thrust of the Reagan tax cut program, when he added, "It may be that proposals of a type that would not conflict with the stimulative nature of his economic program will be presented to him by his advisers or by others, including the leaders of Congress. The president has not invited any such proposals nor have they been presented to him."

Others said that if the president does look at any proposals along these lines it will not be until after the start of the the new year.

The popular Head Start program aims at giving pre-school children from low-income homes a leg up on skills and attitudes needed to succeed in school. Head Start had been called one of the seven essential and untouchable social "safety net" programs by the president earlier this year.

Under the Stockman plan, which Secretary of Health and Human Services Richard S. Schweiker strongly protested, Head Start would have been phased out over four years as a separate program and cut in fiscal 1983 to $780 million.

In addition to rejecting the phaseout, the president reportedly has decided to keep the program going in 1983 at about the same $912 million level as in 1982.

Capitol Hill sources said the president also had decided against phasing out the community development block grants and the urban development action grants, for which Congress authorized about $4.1 billion in fiscal 1983.

Under a plan developed by Stockman and protested by Housing and Urban Development Secretary Samuel R. Pierce Jr., the two programs would have been cut to about $1.2 billion in fiscal 1983 and zero in 1984. Wire service reports yesterday said Reagan had decided to allow $3.8 billion in fiscal 1983 for the grants.

Hill sources also said that the White House had decided to allow 10,000 new units of subsidized housing for the low-income elderly next year, but whether it was allowing any such units for the non-elderly was not clear.

Congress recently has been authorizing 200,000 or more added units of such housing each year, HUD asked for about 100,000 for fiscal 1983 and the OMB proposed none in its initial budget mark-up.

In still another decision, sources said the White House has ruled out a proposed substantial increase in the premium charged to elderly Social Security beneficiaries for the part of Medicare (Part B) covering doctor bills.

The premium is $11 a month, and covers about 24 percent of the cost of the Part B program, which is much smaller than the Part A hospital insurance program, for which the government foots the entire bill.

The proposal had been to raise the premium enough over the next few years to pay 34 percent of total Part B costs, but it has been jettisoned, sources said.

The Part B premium increase was only one of several dozen changes in the basic benefit or so-called entitlement programs, which are among the largest in the budget and which, because they involve almost automatic spending, are different from the discretionary programs subject to the annual congressional appropriations process.

Many experts, including influential Republicans in Congress, say that in addition to dealing with taxes and defense Reagan must cut these to hold down the deficit. They say there is not enough left in the discretionary programs to reach his goals.