The Senate, which six days ago rejected President Reagan's nomination of Robert H. Bork for the Supreme Court, reacted with surprise, caution and skepticism yesterday to Douglas H. Ginsburg, Reagan's new choice for the high court.

Leaders of both parties stopped short of predicting that Ginsburg will be confirmed, and some Democrats suggested that the conservative appeals court judge and former Reagan administration official could run into some of the same troubles that doomed Bork.

Conservatives hailed Reagan's selection. Liberals were critical or noncommittal.

"There's no question conservatives should be happy because this man is a believer in judicial restraint . . . . There's no question that intellectually he's in the big leagues," said Sen. Orrin G. Hatch (R-Utah), a Reagan loyalist who was a key supporter of Bork on the Judiciary Committee.

Sen. Edward M. Kennedy (D-Mass.), who helped lead the fight against Bork, called Ginsburg "an ideological clone of Judge Bork" and suggested the choice reflected the influence of Attorney General Edwin Meese III on the president's thinking.

But most senators, including southern Democrats and moderate Republicans who provided the critical swing votes in the contest over Bork, appeared to be taking a wait-and-see approach, maintaining that they were not familiar enough with Ginsburg or his record to make a quick judgment.

Sen. Arlen Specter (R-Pa.), whose vote against Bork on the Judiciary Committee was regarded as critical, said his initial reaction to Ginsburg's record was "positive" but that he would withhold judgment until he could analyze it further. Sen. Howell Heflin (D-Ala.), another key swing vote on the committee, also withheld judgment.

"I realize that he {Ginsburg} is likely to generate some opposition, but I am not in a position to offer any assessment of his nomination at this point," said Senate Judiciary Committee Chairman Joseph R. Biden Jr. (D-Del.).

Democratic leaders said they would move as quickly as possible to schedule hearings on the nomination but insisted they would not be stampeded into premature action by Reagan's criticism of the Senate's handling of the Bork nomination.

Sources indicated that hearings were possible this year, although Senate floor action appeared unlikely until next year, especially if Congress comes anywhere near its scheduled adjournment date of Nov. 21.

"No one is advocating any unreasonable delay, but the Senate has to take a little time, the {Judiciary} committee has to take a little time," said Senate Majority Leader Robert C. Byrd (D-W.Va.).

Senate Minority Leader Robert J. Dole (R-Kan.) urged that the committee begin hearings "as soon as possible" and said that, "barring major surprises at the hearings," he intends to support Ginsburg. But he made no prediction about Ginsburg's prospects.

Warning against delay, Hatch suggested that Reagan consider calling the Senate back in a special session if it adjourns without confirming Ginsburg. Asked if the White House was considering such a move, Hatch said, "I know they know that's an option."

Both Byrd and Dole sought to cool passions that erupted over the Bork nomination. Dole said the American public would be closely watching the Ginsburg deliberations and urged the Senate to restore a reputation that "suffered a bit in the course of the last nomination."

"I would hope we would stop raking over old ashes, stop pointing fingers, bickering and badgering," said Byrd in a warning that was clearly aimed as much at the White House as it was at the Senate.

Meanwhile, some of the outside lobbying groups that opposed Bork also raised objections to Ginsburg.

John H. Buchanan, chairman of People for the American Way, said the choice was "disappointing," calling Ginsburg's record one of "rigid adherence to Edwin Meese-style conservatism." Kate Michelman, executive director of the National Abortion Rights Action League, said the judge would be rejected if he "proves to be a Bork ideological soulmate with the same hostilities to basic constitutional liberties."

The choice of Ginsburg came was unexpected by many senators, who had expected Reagan to nominate Anthony M. Kennedy, a federal appeals court judge from Sacramento. Some Democrats had urged the nomination of Kennedy as the least contentious choice and were clearly disappointed when he was passed over.

But several Republican conservatives, including Sen. Jesse Helms (R-N.C.), raised strong objections to Kennedy yesterday morning, prompting fears of a filibuster if he was nominated. Helms did not mention Judge Kennedy by name but said he called the White House to object to one of the leading contenders, warning that, as he put it, "no way, Jose, could I support him." Helms expressed pleasure with Ginsburg's nomination.

While liberals were hard-pressed to cite specific details about Ginsburg's record, his support from conservatives, including Meese, fueled their suspicions.

"Judge Ginsburg is a surprising choice, given his age {41} and limited judicial experience," said Majority Whip Alan Cranston (D-Calif.). "He has served on the Court of Appeals for barely a year and received the lowest ABA {American Bar Association} approval rating when he was nominated to the Court of Appeals. There were certainly a number of more qualified and more experienced conservatives on the list being considered. Perhaps they were less acceptable to Attorney General Meese."

Sen. Kennedy made a similar point. "What is most ominous about the nomination at this stage is the suggestion that Ed Meese prevailed upon the president, with little consideration, to name an ideological clone of Judge Bork -- a Judge Bork without a paper trail -- instead of a real conservative who would have broad support in the Senate."

The "paper trail," as Kennedy called it, was regarded as a plus as well as a minus for Ginsburg, whose court opinions and legal writings are far less voluminous that those of Bork, thus inviting charges that he lacks proper credentials for the court. But Bork's writings became a rich vein for his foes to mine and contributed to his rejection by the Senate.

Many Republicans suggested that this, coupled with other factors, including Senate queasiness over rejecting a second nomination on grounds that included ideological considerations, will make it easier for Ginsburg to win confirmation.