Every president has a honeymoon, and Ronald Reagan's has been longer than most. Congress, the press, opinion leaders and even many Democrats are still treating him like a new bridegroom.

But for one important group of Reagan supporters -- the New Right conservatives -- the honeymoon is over.They flexed their muscle over the nomination of Sandra D. O'Connor to the Supreme Court, and lost. o

For some of the most vocal leaders of the New Right movement, the nomination was the latest in a series of slights and insults they have suffered from Reagan advisers which raise questions in their minds about whether the president is really their kind of conservative.

"The White House slapped us in the face," says Richard A. Viguerie, the conservative direct-mail expert. "The White House is saying you don't have a constituency we're concerned about. We don't care about you."

"There's been a challenge issued," explains Viguerie. "It is something we can't ignore. We either fight this one, or we aren't leaders."

Viguerie and his cohorts on the New Right have done just that. They have fumed and fussed. They've launched a series of pointed attacks on O'Connor in their publications and in thousands of letters and telegrams sent to their supporters around the country.

But after two weeks, they have yet to persuade a single senator to come out against O'Connor, the first woman ever appointed to the Supreme Court. They plan to continue what they now see as an all but hopeless fight if only to make it possible to fight and win similar battles in the future.

"In terms of having any real influence with the Reagan administration, we just haven't had any," says Howard Phillips, head of the Conservative Caucus. "All they've done is throw us a few bones to keep the dogs from biting their heels."

The fight is full of irony and goes well beyond the merits of the O'Connor nomination. It is part self-esteem, part coalition politics, part a sense of class conflict between the ideologues of the New Right and the political pragmatists who make up the White House staff.

The roots of the conflict go back to the 1980 campaign, the choice of George Bush as Reagan's running mate, and the emergence of moderates, such as White House chief of staff James Baker III, as key presidential advisers. "We won the election, but lost the White House," many conservatives complained.

Reagan's relations with the New Right have been strained ever since. In this light, the nomination of O'Connor, who on occasion voted with pro-abortion forces as an Arizona state senator, didn't surprise some of the most militant voices on the New Right.

A little background about the New Right and the Old Right is helpful in understanding the conflict. The Old Right comprised traditional economic conservatives, firm believers in the free enterprise system and a strong national defense. It is epitomized by Sen. Barry Goldwater (R-Ariz.), the 1964 Republican presidential nominee.

The New Right accepts the basic philosophy of the Old Right, but has tried to broaden the conservative base to include disillusioned Democrats and nonvoters.

To do this, it devised sophisticated campaign techniques, particularly direct-mail fund raising, and formed a fragile coalition with so-called "social conservatives" -- people opposed to legalized abortion, sex education, the Equal Rights Amendment, "humanism," general permissiveness, gun control, and a host of other religious and social issues.

In numbers, the coalition is relatively small -- Viguerie, one of the movement's founders, estimates it can mobilize no more than 5 to 7 1/2 percent of the electorate. But, like the liberal wing of the Democratic Party, it is noisy and rigid philosophically.

Reagan, in his campaign, played to the basic goals of the New Right coalition with his litany of "family, work, neighborhood, freedom, peace." He endorsed a constitutional amendment banning abortion. Anti-abortion groups flocked to his banner, although leaders of the New Right like Biguerie joined his bandwagon only after other candidates fell by the wayside.

But as president, Reagan has a different agenda, and his administration had distanced itself from the New Right."On issues like abortion, school prayer and some of these, my personal view is that they're somewhat peripheral to some of the things that national government should be concentrating on," one top White House adviser said during a recent luncheon at The Washington Post.

New Right and anti-abortion spokesmen blame this on a betrayal of confidence and a failure to understand their coalition. There is a strong element of class and cultural conflict to this.

"From the very outset, the administration has been staffed by country-club conservatives who have contempt for social conservatives. The White House has a tendency to treat us as a sort of minority group," says Phillips of the Conservative Caucus. "We aren't the Skull and Bones crowd."

"The White House doesn't understand our coalition," says Viguerie. "The social conservative isn't someone they'd invite to their home, or country club. The whole social conservative thing isn't their cup of tea."

Kevin Phillips, a conservative theorist, offered another analysis in a recent issue of his American Political Report newsletter. Candidates used New Right and anti-abortion themes in 1978 and 1980 elections because voters agreed with their general critique of moral decay and permissiveness in the country, Phillips noted.

"The neo-Puritan minority was able to mobilize its issue activists with little backlash," he wrote. "That equation is changing now with Reagan in the White House. General public sympathy for a further move to the right on moral issues is less, and more attention is focusing on less popular specific proposals."

No other single issue is as important to the New Right coalition as abortion. It is the glue that holds much of the coalition together, that attracted northern blue-collar Catholics and southern evangelicals, most of whom are traditional Democrats, to the New Right and its candidates.

Anti-abortion activists view abortion as the great civil-rights issue of the era, the litmus by which to judge all officeholders. O'Connor, because of some seemingly pro-abortion votes in the Arizona Senate, failed the test.

They viewed her nomination as a direct assault. To preserve the coalition, other New Right groups had little choice but to rally to the defense. In coalition politics, an attack on one is an attack on all.

Within two days of the nomination, about 20 conservative groups, most loosely affliated with the New Right, came out against O'Connor. Among the best known of them was the Moral Majority. The symbolism was confusing. Judge O'Connor, after all, was supported by the nation's two best known conservatives, Reagan and Goldwater, her Arizona neighbor.

What was going on?

An unusual coincidence of personalities had a great deal to do with the response. The key figure was Dr. Carolyn Gerster, a woman remarkably similar in background to Judge O'Connor. Like O'Connor, she is an aggressive, attractive and publicly spirited individual, a trail-blazer of sorts who launched a professional career at a time when few woman did so. And like O'Connor, she lives in the Phoenix suburbs.

In the 1970s, she was an anti-abortion lobbyist who considered then state senator O'Connor a pro-abortion adversary. By 1980, physician Gerster had become president of the National Right to Life Committee, the nation's largest anti-abortion group, and she had a one-on-one meeting with Reagan in early January. During that meeting, she claims Reagan pledged he would never appoint a supporter of legalized abortion to the Supreme Court.

Gerster and her allies did a quick research job on O'Connor's legislative record over the July 4th weekend when the possibility of her nomination first leaked out. After finding four instances where O'Connor allegedly cast votes supporting legalized abortion, Gerster fired off a telegram to Washington July 6 requesting the White House not make a decision on the nomination until a package detailing information about the votes reached Washington the next day.

Meanwhile, she contacted other anti-abortion leaders who mounted an anti-O'Connor campaign. But Reagan announced O'Connor's nomination before the packet arrived in Washington. Gerster was shocked. She and other anti-abortion leaders, who had supported Reagan during the presidential campaign, felt the president had betrayed promises he had made to them and the Republican platform.

They felt they had a stake in Reagan's presidency. "We induced millions of Democratic voters to cross over for Mr. Reagan and other pro-life senators," declared Dr. J. C. Wilke, president of the National Right to Life Committee.

Human Events, a conservative newspaper normally friendly to Reagan, said conservatives around the country were "astonished an dismayed" by the nomination of anyone with "such murky ideological moorings."

More militant voices threatened reprisals against Republican congressional candidates in 1982. "I don't mind holding a grudge and carrying out a vendetta," said Paul Brown of the American Life Lobby. "The loose-knit coalition we have with the White House may be destroyed. I'm not at all adverse to making up a hit list for 1982 made up entirely of Republicans."

But others see hope of making peace with the Reagan White House. "If the White House shows it views the pro-family movement as an important part of its coalition, then the situation is salvageable," says Paul Weyrich, a leading New Right strategist. "But if they wall themselves up and take the position that any opposition means you're not part of the Reagan team then we may be in trouble."

Few on the New Right see any realistic hope of blocking O'Connor's confirmation in the Senate. But most agree they have made a point.

"No matter how many votes we get in the Senate, the administration won't make the same mistake next time," says Phillips of the Conservative Caucus.