WASHINGTON--Anthony M. Kennedy's Supreme Court nomination is clearing early obstacles to Senate confirmation, with a conservative Republican dropping potential opposition and a leading Democrat declaring "his prospects are good."

Kennedy's nomination was in even better shape Thursday than when it began the day before, as a new spirit of cooperation pervaded the White House and Congress after two earlier nominees failed.

In a great relief to Kennedy and the White House, prominent conservative Sen. Jesse Helms, R-N.C., declared after meeting with nominee, "I think he'll make a fine member of the Supreme Court."

Helms, who two weeks ago left the impression he could filibuster against the federal appellate judge, said he wouldn't make a final decision until the Senate Judiciary Committee completed confirmation hearings.

But Helms said he felt "very comfortable" after meeting the 51-year-old jurist from Sacramento, Calif.

"He's a very impressive gentleman," Helms said. "I was pleased with what I heard."

President Reagan also met with Helms to reassure him about the nomination. Reagan also chatted amiably with Judiciary Committee Chairman Joseph R. Biden Jr., D-Del., who led the successful fight to defeat the first nominee for the court vacancy, Robert H. Bork. Reagan's second nominee, appellate judge Douglas H. Ginsburg, asked the president to withdraw his name last Saturday after Ginsburg's admission of past marijuana use.

Biden said Reagan requested early confirmation hearings, and the senator told reporters he would try to comply. "I know of no one who wants to move this slowly," he said.

And Biden added that "his prospects are good, based on what we've read and heard so far" from judges, students taught by Kennedy in law school and attorneys. But he cautioned there is much still unknown about his more than 400 written opinions, and pointed out an American Bar Association review and comphrensive FBI checks are weeks from completion.

Biden said he and the commitee's ranking Republican, Strom Thurmond of South Carolina, would meet with the Senate leadership on a hearing timetable, and then sit down "sometime next week" with White House chief of staff Howard H. Baker Jr.

Thurmond, who met with Reagan along with Biden, predicted that conservatives in general would support Kennedy--even though Thurmond said two weeks ago that some conservatives were uneasy with Kennedy's record as a conservative judge.

Kennedy was busy Thursday making courtesy calls on Capitol Hill. During a meeting with Senate Republican Leader Bob Dole of Kansas and other GOP leaders, Kennedy said: "I like this. It's been wonderful."

Thurmond said he was not aware of anything in Kennedy's background that would surprise senators, but he added, "You never can tell."

Dole said: "The Senate's ready to move ahead. I don't see any partisanship."

Kennedy also met with Senate Majority Leader Robert C. Byrd, D-W.Va..

Kennedy told Reagan and FBI investigators there was nothing lurking in his past, White House Spokesman Marlin Fitzwater said.

Among other things, FBI agents looked into Kennedy's one-time position as a lobbyist for a liquor distiller, a record company and opticians.