Conservative feuded yesterday over the nomination of Sandra D. O'Connor to the Supreme Court, while her White House and Capitol Hill supporters expressed confidence that she will be confirmed.

"I don't think there's any problem," said White House counselor Edwin Meese III.

"I intend to support her," said Senate Judiciary Committee Chairman Strom Thurmond (R-S.C.), unless something comes up."

As they spoke, however, about 60 leaders of the New Right were holding an emergency meeting to mobilize opposition to the nominee because of their objections to her position on abortion.

And as they were meeting, conservative Sen. Barry Goldwater (R-Ariz.) was saying that one of their leaders, Jerry Falwell, deserves a "kick in the ass" for his opposition to O'Connor.

The furor stemmed from several votes O'Connor cast while serving in the Arizona Senate. In one instance, she voted against a football stadium bill that carried a rider prohibiting abortions at the University of Arizona Hospital.

Anti-abortionists opposing her nomination charged that the also supported the legalization of abortion in Arizona in 1970, before the Supreme Court legalized it for all the states in 1973. The 1970 action, however, come on an unrecorded voice vote, according to legislative officials.

Whatever its outcome, the controversy was an important event in Reagan's Washington, for it cleanly split the president from parts of the coalition that helped elect him and, if only for a moment, gave him a new constituency of liberals who praised the nomination.

Most Capital Hill observers agreed that confirmation is likely. But many also said it might entail O'Connor's going before the Senate Judiciary Committee and, as one put it, "announcing her conversion" on the abortion question.

Early comments by O'Connor on another controversial issue, state aid to private schools, also surfaced yesterday. In a 1970 interivew for Phoenix magazine, O'Connor was quoted as saying that such aid was "clearly unconstitutional."

But yesterday's debate centered on abortion. "We feel we've really been challenged on this," said conservative direct-mail king Richard Viguerie. "The conservatives weren't consulted. They just said 'like it or lump it.' I haven't talked to a conservative yet who wasn't disturbed by this."

"The president is going to be suffering a degree of political influenza from which he will not easily recover," added Conservative Caucus Chairman Howard E. Phillips. "It will be a costly fight with people who have been his most faithful supporters."

Phillips said the action might cost Reagan support from conservatives on other issues, such as his economic proposals. "We're going to be redirecting our efforts somewhere else now," Phillips said.

Through the White House would like quick confirmation hearings and an early vote to avoid too much bloodletting, hearings probably won't begin until late July. Confirmation might then come in September, after the August recess.

Some Senate conservatives, ordinarily allies of the New Right organizations, yesterday said they will support the nomination unless something new comes up to dissuade them.

Sen. Orrin G. Hatch (R-Utah) said the president "has assured me personally that she offered her support for the Republican platform," including the sections on the sanctity of the American family. "I also have real questions whether any single issue should be able" to stand in the way of a Supreme Court appointment.

"When Barry Goldwater and Ronald Reagan say she's conservative," Hatch said, "that's hard to question."

Sen. John P. East (R-N.C.), another abortion opponent, said he would withhold judgment until the confirmation hearings. East and Hatch emphasized that O'Connor will be questioned closely about her views then.

Goldwater's comments about the opposition to his friend, O'Connor, were more colorful. "I am probably one of the most conservative members of Congress, and I don't like to get kicked around by people who call themselves conservatives on a nonconservative matter. It is a question of who is best for the court. If it is going to be a fight in the Senate, you are going to find Old Goldy fighting like hell."

Goldwater's comment about Falwell came when asked about an earlier comment from the Moral Majority leader that all good Christians should be concerned by the appointment.

"I think every good Christian ought to kick Falwell right in the ass," Goldwater said.

Meese said he did not think the opposition would hurt the nomination. "I think a record on these subjects and her personal viewpoints" will calm the opponents. "With her overall excellence and judicial approach to things . . . I don't think there's any problem with her confirmation," he said.

The opposition could benefit the Reagan administration in some ways by separating it from the single-minded anti-abortion lobby and broadening the potential base of support to include many moderate Democrats offended by the right.

O'Connor's comments on state aid to private schools were reported in a profile that appeared in Phoenix magazine in 1970. It described her as "almost alone in the Arizona Senate in opposing publicly state aid to private schools" though she was a trustee of one, Phoenix Country Day School. "'Clearly unconstitutional,'" the magazine quoted her as saying.