Supreme Court nominee Sandra D. O'Connor went politicking on Capitol Hill yesterday, expressing her opposition to abortion and winning a prediction from the leadership that she will be confirmed without difficulty.

The Moral Majority also backed away from its earlier opposition, acknowledging that confirmation is inevitable. "We should have shut up and not said anything," said spokesman Cal Thomas. "We are working very hard to fall in line behind the president."

Though other anti-abortion groups held fast, yesterday nevertheless looked like the day everything began to fall in place for the nomination. O'Connor, carefully briefed and accompanied by a flying wedge of Reagan administration officials, made her way from office to office for brief chats and photo sessions.

After each stop, a senator would generally emerge to say how impressed he was with O'Connor. Then, trailed by about 60 reporters, camera technicians, sound crews and police officers, she would go off to the next place. Publicly, she would only say that the day was going "wonderfully."

"I'm just going around to have a chance to say hello, face to face," she said. "I understand it's traditional."

Privately, however, both O'Connor and the Reagan administration were moving fast to defuse the abortion issue. Sen. Dennis DeConcini (D-Ariz.), a Judiciary Committee member, said she discussed abortion with him and with Sen. Strom Thurmond (R-S.C.), Judiciary chairman.

"She reasserted what she had told me last week. she said she was opposed to abortion."

It was also learned yesterday that Reagan political aides were telling conservatives that she believes abortion regulation is a "legitimate subject" for legislation at the state level.

According to Young Americans for Freedom officials James V. Lacy and Bob Heckman, White House aide Lyn Nofziger, at a meeting last Wednesday, displayed a summary of the president's conversation with O'Connor to illustrate her position.

Heckman quoted the summary as saying O'Connor finds "that abortion regulation is a legitimate subject for legislation." Nofziger, who could not be reached for comment, reportedly added the word "state" in elaborating on the summary.

That is about as specific as the White House has been in describing her views. It is not necessarily inconsistent with the Supreme Court's 1973 abortion ruling, which allowed the states to regulate abortion after the first three months of pregnancy.

O'Connor's day began at the Justice Department, where she met with Attorney General William French Smith and his aides. O'Connor, Smith, aides and two White House lobbyists, Max L. Friedersdorf and Powell A. Moore, then met separately with Thurmond, Senate Majority Leader Howard H. Baker Jr. (R-Tenn.), Minority Leader Robert C. Byrd (D-W. Va.), House Speaker Thomas P. (Tip) O'Neill Jr. (D-Mass.), Senate Judiciary Committee members DeConcini and Joseph R. Biden Jr. (D-Del.), House Minority Leader Robert H. Michel (R-Ill.) and other house Republicans, and her friend, Sen. Barry Goldwater (R-Ariz.).

The half-hour with Thurmond was probably the longest encounter of the day. "I would judge that she would be confirmed," Thurmond said afterward. "I've heard very little opposition to her around the Hill. She's a very impressive lady. She has excellent credentials. I expect to support her."

Thurmond and Baker said it would be difficult to hold confirmation hearings by the end of July, as the administration requested. Both said the process probably would begin after the August recess.

The Moral Majority's half-turn on the O'Connor nomination followed its confrontation last week with Goldwater, who said that "every good Christian should Kick Jerry Falwell in the ass" for Falwell's opposition to the nomination.

The PR fallout has been incredible." Falwell spokesman Thomas said yesterday. He said the group had been assured that "some of our friends in the Senate, conservative members, will be asking questions of Judge O'Connor that had concerned us. . . . We are working very hard to fall in behind the president."