Supreme Court nominee Anthony M. Kennedy sailed smoothly through his first day of Senate scrutiny yesterday as key conservatives praised him and Judiciary Committee Chairman Joseph R. Biden Jr. (D-Del.) said his chances for confirmation are "very good."

Although many senators remained wary in light of the troubles that doomed President Reagan's two previous court choices, hardly a negative word was spoken about the 51-year-old federal appeals court judge from California making his first rounds on Capitol Hill.

Among those favorably impressed was Sen. Jesse Helms (R-N.C.), who earlier threatened to oppose Kennedy in apparent hopes of winning the nomination for a more conservative jurist, giving rise to fears that he might filibuster if Kennedy were named.

"He's a very impressive gentleman . . . . I was pleased with what I heard . . . . I think he'd make a fine member of the Supreme Court," said Helms after meeting with Kennedy.

As Kennedy paid courtesy calls on Senate leaders, there was little of the partisan rancor that accompanied Reagan's earlier nominations of Robert H. Bork, whom the Senate rejected, and Douglas H. Ginsburg, who withdrew after admitting he had spoked marijuana as a student and law professor.

"We'll approach it {the Kennedy nomination} in a cooperative and constructive way and see how that works," said White House chief of staff Howard H. Baker Jr., whose nonconfrontational approach toward Congress finally prevailed in the choice of Kennedy after the failure of the two more controversial nominees.

Democrats also appeared reluctant to engage in another battle, although they continued to insist that Kennedy would be subject to intense scrutiny.

Striking an accommodating note, Biden said: "I've heard nothing particularly negative about Judge Kennedy at all. So thus far his prospects seem very good and I hope they will continue."

Biden said this observation was based on "what we've heard and read so far," including comments from lawyers, students and other judges, and that no final conclusions can be drawn until investigations are completed by the FBI and a review panel of the American Bar Association.

Minority Leader Robert J. Dole (R-Kan.), who had earlier accused the Democrats of partisanship in the Bork nomination, said he saw no partisan strife emerging with the Kennedy nomination. "I think the Senate is ready to move ahead . . . . I don't see any partisanship," he said, describing Kennedy as an "outstanding choice."

Sen. John S. McCain III (R-Ariz.) said the Senate was simply "weary" of fighting over court nominees. "Nobody wants to go through that again. There's just too much blood on the floor," he added.

Kennedy reflected the changed mood as well. As he met with Dole and other GOP leaders, he smiled broadly at reporters and said, "I like this. It's been wonderful. I've had a great reception in Washington."

But some bickering continued over whether the Judiciary Committee should begin confirmation hearings before the Senate recesses for Christmas or wait until it reconvenes, probably in early January.

Biden and Sen. Strom Thurmond (R-S.C.) discussed the timing issue yesterday with Reagan who urged the committee to begin hearings as soon as possible.

Thurmond continued to insist they could start before Christmas. But Biden, who earlier said that starting before January was unlikely, reported after the meeting that no decision had been made.

"We're all anxious to do it as quickly as we possible can . . . I know of no one who wants to move this thing slowly," Biden said.

One factor in scheduling the hearings is how long it will take the ABA's judicial review panel to scrutinize Kennedy. Biden and other committee Democrats have said they want the results of the ABA's investigation in hand before beginning hearings.

Former judge Harold R. Tyler Jr. of New York, chairman of the ABA's standing committee on the federal judiciary, said yesterday that the panel is trying to expedite its review and hopes to complete it by the end of this month or the first week of December.