Education Secretary William J. Bennett, in a telephone call cleared with President Reagan, yesterday urged Supreme Court nominee Douglas H. Ginsburg to withdraw in the wake of his admission that he had smoked marijuana.

Loye Miller, a spokesman for Bennett, said Ginsburg told Bennett he was surprised by the call because he had been to the White House earlier in the day and thought he had received encouragement. Miller said Bennett replied that he would not be making the phone call had the president done anything to discourage him. Another Education Department spokesman said Reagan had told Bennett, "Do what you think is right."

Ginsburg did not indicate to Bennett what he intended to do, according to the spokesmen.

Support for the eight-day-old nomination appeared to be crumbling throughout the day yesterday. A White House source said several conservative senators privately urged the administration to withdraw the nomination. "It's clear that Judge Ginsburg cannot be confirmed," a White House official said last night.

Early in the day the White House sought to play down the significance of Ginsburg's disclosure Thursday night that he had smoked marijuana "once as a student in the 1960s and on a few occasions" in the '70s. Reagan, vowing to stand behind his nominee, said the federal appeals court judge "was not an addict" and predicted that the American people will be "compassionate" and forgive Ginsburg's "youthful error."

But asked in an interview with several news organizations whether he would have nominated Ginsburg had he known of his marijuana use, Reagan said, "I don't know whether that would have made a shade of difference or not . . . that might have, I don't know."

Attorney General Edwin Meese III -- who urged Reagan to choose Ginsburg -- said that Ginsburg's disclosure "should be a factor" in Senate consideration of his nomination, Reuter reported. Meese, in Cambridge for a speech to a law enforcement group, said Ginsburg's nomination should not be withdrawn but that his marijuana use "certainly is not a positive factor."

Senate Majority Leader Robert C. Byrd (D-W.Va.) said Ginsburg should give "very, very serious consideration" to withdrawing, and other senators of both parties indicated Ginsburg's use of marijuana could complicate or doom his already faltering chances for confirmation.

The Senate response cut across usual political and ideological lines as some Democratic liberals joined Ginsburg's most ardent supporters on the Republican right in contending that the latest disclosure, taken alone, should not disqualify Ginsburg from elevation to the Supreme Court.

However, conservatives continued to criticize Ginsburg's conduct, an indication that the core of his support was eroding.

Even as Ginsburg's drug use was debated yesterday, questions arose about whether he had adequate courtroom experience and whether he misled the Senate Judiciary Committee last year about the extent of that experience.

Justice Department spokesman Terry H. Eastland acknowledged yesterday that Ginsburg's total courtroom experience amounted to one appeals court argument, lasting about one hour.

When nominated for a judgeship on the appeals court here last year, Ginsburg, asked on a questionnaire how many cases he had "tried to verdict," answered 34. He noted that he was using figures for "all litigation conducted by the Antitrust Division" during his 20 months there, and not cases he had personally tried.

Ginsburg also said he had "appeared in court frequently through the indictments, informations, and briefs that I have caused or authorized to be filed on behalf of the United States."

Eastland said the cases Ginsburg listed were those "he was supervising in a managerial position."

Yesterday attention focused on why Ginsburg had not disclosed to administration officials the fact that he had used marijuana and whether he had ever been asked specifically about it.

Sen. Arlen Specter (R-Pa.) said Ginsburg told senators he has used marijuana as recently as 1979, while a professor at Harvard Law School. Ginsburg joined the Reagan administration four years later, as a deputy assistant attorney general in the Antitrust Division.

An administration official said Ginsburg was asked in an interview with Meese and other high-ranking administration officials the night before Reagan selected him whether there was anything in his background that might endanger his confirmation. Ginsburg did not disclose his marijuana use, the source said, and he mentioned only that he had strained relations with his ex-wife.

Eastland said he had found no evidence that Ginsburg was ever asked about drug use, "whether on employment forms related to government service or in interviews conducted by the FBI or other Justice Department and White House officials."

A Justice Department official said that, under the policy currently in effect, "Ginsburg couldn't be hired now as an assistant U.S. attorney." The official said that although minor use of marijuana in college does not disqualify an applicant, "any illegal drug use after being admitted to the bar" would rule out hiring.

Under a form put into use in April 1986, all applicants for jobs as federal prosecutors are asked whether they have ever used drugs and to specify what kinds, when and how frequently, Eastland said.

The Federal Bureau of Investigation, which failed to uncover evidence of Ginsburg's marijuana use during five inquiries for federal jobs -- including two extensive background checks -- said agents ask about drug abuse but that "results are largely dependent upon the integrity of those interviewed during the investigation." The FBI does not interview the subjects of background checks.

FBI sources said they were never told about marijuana use when they interviewed his friends and colleagues in Cambridge. Harvard Law School Prof. Hal Scott, who described himself as Ginsburg's close friend for more than 25 years, said he did not tell the FBI that he knew of one incident in which "Doug smoked a marijuana cigarette" at a party during the 1970s because, he said, "I had forgotten about this until yesterday."

If those interviewed by the FBI are found to have deliberately lied, they could be subject to prosecution. The maximum penalty for willfully making a "false statement" to an FBI agent is five years in prison and a $250,000 fine.

In comments yesterday morning, Reagan said he was not concerned about Ginsburg's admitted drug use.

"I'm satisfied with his statement," Reagan said. "He was not an addict" and "I'm sure there were a great many people who did that {during} that particular period."

Reagan said "the message it sends" to young people "is that he says he regrets and shouldn't have done it. I think it's a helpful message."

In a later speech to ethnic and minority leaders, Reagan cited Ginsburg's "obviously remarkable credentials." He said many of the country's most prominent public servants "have had to acknowledge errors they made in their youth or even more serious errors committed when they were older" and have been forgiven by the American people.

"In the case of Judge Ginsburg, I think the American people will be no less compassionate and no less wise," Reagan said. "Judge Ginsburg erred in his youth. He has acknowledged it. He has expressed his regrets."

Nancy Reagan, who has crusaded vigorously against drug abuse with her highly publicized "Just Say No" program, said in a statement, "Unfortunately the '60s and '70s were a time when a lot of people experimented with pot. Apparently he did, and I'm sorry about that."

Ginsburg can expect a thorough grilling on the drug-use issue by the Judiciary Committee during the hearings on his confirmation scheduled to begin the week of Dec. 7, and some said Senate action on the nomination appears virtually impossible before year's end.

In criticizing Ginsburg's conduct and suggesting he consider withdrawing, Byrd departed from the cautious approach he took toward Reagan's earlier nomination of Judge Robert H. Bork for the high court vacancy created by the retirement of Lewis F. Powell Jr.

Noting that the Reagans have waged a major campaign against drug use, Byrd said: "The thing that concerns me about it is the image that a Supreme Court justice presents to the young people of this country. It wasn't just a youthful indiscretion. He did it when he was a law professor and it was illegal . . . . It's most important; it's not irrelevant."

Byrd's comments were made only moments after Senate Judiciary Committee Chairman Joseph R. Biden Jr. (D-Del.) suggested that use of marijuana in the '60s and '70s was "irrelevant" in light of its widespread use among young people at the time. He said the furor was obscuring more important constitutional issues, such as Ginsburg's interpretation of privacy rights.

Sen. Howard M. Metzenbaum (D-Ohio), who met with Ginsburg for more than an hour yesterday as he wound up his courtesy visits with members of the Judiciary Committee, also brushed off the drug issue, saying the two had a "quite satisfactory discussion" of "far more important issues," including his basic constitutional philosophy.

But Sen. Larry Pressler (S.D.), a moderate Republican who supported the nomination of Bork and other conservative judges, said he would have a "very hard time" supporting Ginsburg, whom he described as "hard to defend in my state."

Pressler said he was urging the White House to "reassess" the nomination. Several other Republicans, including Sen. Warren B. Rudman (N.H.), have indicated they would welcome such a move. "He {Ginsburg} has to make that choice," said Sen. James A. McClure (R-Idaho), a conservative who said the drug use is a "serious issue" that the Senate would have to consider.

Sen. Patrick J. Leahy (D-Vt.), a Judiciary Committee member, said the drug-use controversy probably precludes Senate action this year. "Two days ago I would have said I was pretty sure we'd have confirmation this year. With this, I would say the chances of confirmation are really dimming" for this year, he said.

"The White House rushed its selection," Metzenbaum said. "The committee should not rush its decision."

Leahy, like most other Democrats, was hesitant to criticize Ginsburg on the marijuana issue alone but suggested it was having an effect "because so little is known {about Ginsburg} that anything that comes out will create a stir," as Leahy put it.

But he also suggested it showed a "double standard" on the part of conservatives when it comes to judicial nominees. "If this were a liberal nominee, they would be saying 'hangin' ain't good enough,' " Leahy said.

Other Democrats were content to let the Republicans do all the talking. Sen. Edward M. Kennedy (D-Mass.) just smiled and waved when reporters asked him for comment. When asked for his reaction, Sen. John H. Glenn (D-Ohio) borrowed the words of Nancy Reagan's antidrug campaign and said, "Just say no."

Sen. Steven D. Symms (R-Idaho), a conservative, described the situation as "unfortunate" but likened Ginsburg's conduct to underage teen-agers sneaking a beer and criticized opponents for "holier-than-thou self-righteousness."Staff writers Helen Dewar, Al Kamen and Mary Thornton contributed to this report.