At 9 a.m. last Nov. 24, four of the most restive leaders of the New Right met in the White House with presidential chief of staff James A. Baker III and presidential counselor Edwin Meese III.

High on the list of topics discussed were the 1982 elections and the New Right's social agenda of busing, school prayer and abortion, all of which the Reagan administration had gingerly avoided during its first year in office.

Baker pleaded for patience, promising that the administration would get around to the controversial social issues in early spring, according to one New Right leader present. "He said not to worry. We're on your side."

Now, 5 1/2 months later, the administration has begun fulfilling that promise.

This week the president endorsed a constitutional amendment to permit prayer in schools, and the Justice Department gave its blessing to an anti-busing bill. Earlier, the president also had endorsed legislation providing tuition tax credits for private schools and wrote a conciliatory letter to anti-abortion leaders.

The actions may be more symbolic than substantive. All the initiatives face major obstacles. Amending the Constitution the way Reagan has proposed, for instance, requires approval by two-thirds of both houses of Congress and of 38 states, a time-consuming and risky process.

But the moves have had one desired effect: they solidified support for Reagan among uneasy New Right conservatives.

"We think the president has done exactly what he always promised he'd do," Cal Thomas, communications director of the Moral Majority, said yesterday. "As for the 1982 elections, he has given us a very strong base for us to say the president is addressing social issues."

Rev. Jerry Falwell, who heads the Moral Majority, plans to kick off this effort with a national telecast on school prayer to be broadcast Sunday night.

The issues Reagan picked to emphasize and the way he has done so are an instructive example in presidential politics.

The tuition tax credit and school prayer announcements were well orchestrated and highly public. The one on tuition tax credits was made before Roman Catholic clergymen in Chicago; the one on school prayer before Christian fundamentalists at the White House.

They were the least controversial items on the New Right agenda.

"It is easy for the White House to endorse something like school prayer which has the support of a majority of the public, and alienates no major Reagan constituency," said Howard E. Phillips, chairman of the Conservative Caucus and one of the New Right leaders at the Nov. 24 meeting.

"It was something the conservatives and pragmatists at the White House could agree on. It is a no-lose situation for them."

On busing, a more complex issue which tied up the Senate for weeks last year, the administration announced its position by simply releasing a letter written by Attorney General William French Smith without prior warning Thursday.

Reagan was even more cautious on abortion, an issue that deeply divides the country and his Republican Party. He addressed it by sending a generally worded letter to anti-abortion leaders in early April urging them to unite behind one of the two major anti-abortion measures before Congress.

The politics are clear. Conservative political operatives have been urging action on school prayer for months, arguing it would give Republicans congressional candidates an issue to attract support among Christian fundamentalists, particularly in the South. The electoral strength of this group is debatable, but the Moral Majority claims to have brought 2 million new voters into the political process in 1980.

Some candidates are already using the school prayer issue. In Tennessee, for example, Rep. Robin L. Beard (R-Tenn.) has accused incumbent Sen. Jim Sasser (D-Tenn.), whom he is trying to unseat, of being soft on the issue although Sasser claims to have cast pro-prayer votes 12 of the 13 times it has come to the floor during his term.

The anti-busing bill, which would severely restrict the use of busing by the federal courts as a remedy for segregated schools, presented more difficult problems.

The legislation is sponsored by the Right. But it involves race, where the administration's track record has been most severely criticized, and it involved what the organized bar and some within the Justice Department and, indeed, the White House, regard as a potentially dangerous tampering with the independence of the federal judiciary.

The department's handling of the issue in its long-awaited opinion Thursday reflected that dilemma as well as what Justice Department sources described as a long and unusually vigorous internal fight.

Capitol Hill observers in both parties called the position issued by Smith "mush."

At first glance, Smith appeared to be saying that the busing restriction could pass constitutional muster. But yesterday, both sides in the debate were interpreting the opinion to their liking. Sen. J. Bennett Johnston (D-La.), a co-sponsor with Sen. Jesse Helms (R-N.C.) of the busing rider, hailed Smith's statement as a "major victory."

David Landau, American Civil Liberties Union lobbyist and an opponent of the busing proposal, saw it as including "some very positive things from our point of view."

In fact, House Judiciary Committee Chairman Rep. Peter W. Rodino Jr. (D-N.J.) had asked for the "views" of the Justice Department. What he got, in the view of one committee observer, was a "cut-and-paste job" on the constitutionality of the bill.

"They didn't say whether they support the bill," said a committee aide.

Smith said the bill was constitutional insofar as it restricted only the lower federal courts rather than the Supreme Court and the state courts. In fact, members of Johnston's staff said their bill is intended to restrict the Supreme Court.

Without that restriction, the legislation becomes relatively toothless, allowing the Supreme Court to call the shots on busing just as it does now. Smith's opinion also said such a proposal probably would pass muster only if it did not prevent federal courts from imposing busing when busing is the only way to remedy a constitutional violation.

Who would determine that? The federal courts.

A second opinion issued Thurday by Smith, on the constitutionality of a bill to withdraw federal court jurisdiction over school prayer issues, also left gaps.

Smith said, "Congress may not . . . consistent with the Constitution, make exceptions to Supreme Court jurisdiction which would intrude upon the core functions" of the court. He did not, however, say whether he thought the school prayer restriction involved one of these "core functions."