The Supreme Court nomination of Robert H. Bork was put in jeopardy yesterday when three southern Democrats and Sen. Arlen Specter (R-Pa.), the only undecided Republican on the Senate Judiciary Committee, announced they will oppose confirmation.

The announcements by Democratic Sens. Terry Sanford of North Carolina, David H. Pryor of Arkansas and especially J. Bennett Johnston of Louisiana signaled that the White House strategy of winning strong support for the nomination from southern Democrats has failed. Johnston predicted "overwhelming" opposition from other southerners and called on President Reagan to withdraw the nomination.

He said there is now "a certain inevitability" to Bork's defeat, adding, "My guess is this nomination is going to fall apart and we'll be talking about alternative names."

Reagan vowed yesterday to continue pressing for Bork's confirmation, but some White House strategists acknowledged privately that the fight seems lost. The president does not believe the nomination should be withdrawn, according to one source, and no decision on his next step will be made until after a meeting with undecided senators today. {Details on Page A14.}

Specter's announcement that he will also vote against confirmation because of Bork's "repeated and recent rejection of fundamental constitutional doctrines" came in midafternoon after Sanford, Pryor and Johnston had made their statements, and was another blow to the administration.

As the only moderate, undecided Republican on the Judicary Committee, Specter had a high profile during the hearings on the nomination as he relentlessly grilled Bork and other witnesses on complex questions of constitutional interpretation.

The sudden stampede against Bork was characterized by Senate Minority Whip Alan K. Simpson (R-Wyo.) as "an orchestrated effort" to produce "the defector of the day" and create an atmosphere that could doom Bork's chances. White House officials, describing Reagan as determined to salvage the nomination, insisted there was still time to reverse the tide against Bork.

"It's a tough fight, but I think we're doing well and we're going to keep going," Attorney General Edwin Meese III said after he and White House chief of staff Howard H. Baker Jr. met with Senate Republican leaders and all GOP Judiciary Committee members except Specter.

But Bork's allies were unable to produce any defectors of their own, and a new poll of public opinion in 12 southern states lent credence to Johnston's prediction of solid opposition to the nomination by southern Democrats.

The poll by the Roper Organization, published yesterday by the Atlanta Constitution, said southerners oppose the nomination by 51 percent to 31 percent. More important, the poll suggested that the opposition is broad as well as intense. Bork's confirmation was opposed 46 to 34 percent by southern whites, 47 to 38 percent by men, 54 to 24 percent by women and 44 to 39 percent by self-described conservatives, according to the poll.

Bork's support did not exceed 40 percent in any of the states, the Roper poll said. The latest Washington Post/ABC News Poll showed opposition to Bork's confirmation among southern whites rising from 25 percent in August to 41 percent in mid-September.

"Bork's support has been slipping every single day," an aide to a southern Democratic senator said. Other sources said the results of the Roper poll in the South had been circulated among southern Democrats before their publication yesterday.

Johnston's decision, announced at a noon news conference, was the clearest indication that Bork's nomination is in serious trouble. A senior member of the Senate with ambitions to succeed Majority Leader Robert C. Byrd (D-W.Va.), Johnston was thought unlikely to move early against Bork unless he was certain of solid support, including that of his fellow southern Democrats.

Reflecting the deep and passionate divisions in his state over the Bork nomination, Johnston went out of his way to stress his decision had nothing to do with the abortion issue. Bork was strongly backed by "right-to-life" groups, but Johnston said that opponents of abortion who viewed Bork as "some sort of savior" should also "look at his writings -- his lack of occupation with morals and religion."

Before the hearings, Time magazine said Bork was an agnostic, a description he denied during his testimony.

Johnston said Bork's stated views on a number of issues, particularly civil rights questions, showed that his was "a scholarship devoid of moral content. He misses the spirit of the Constitution."

He said another factor was that Bork, a native of Pittsburgh, was nominated to replace retired Justice Lewis F. Powell Jr., who was the high court's lone southerner. "We've always had a southerner on the court and we ought to have one now," Johnston said.

The generally conservative southern Democrats have long been recognized by both sides as the pivotal bloc of votes in the Bork confirmation fight. Opposition by most of them, as Johnston predicted, would virtually doom Bork's nomination.

Going into the battle, Bork's opponents could count on a base of about 29 votes against confirmation among Democrats who last year voted against elevating Justice William H. Rehnquist to chief justice. Some of these mostly liberal Democrats have not announced how they will vote on the Bork nomination, but there have been no signs of cracks in this base.

In addition, five of the six freshmen Democrats from outside the South are considered virtually certain to oppose confirmation. Sen. Bob Packwood (R-Ore.), the first Republican to voice opposition to Bork, said earlier this week that at least two more Republicans would join him. Packwood's list of opponents did not include Specter, raising the number of likely GOP defectors to at least four.

Along with Johnston, Pryor and Sanford, the likely opponents total 41 votes. If the remaining eight uncommitted Democrats in five states -- Alabama, Arkansas, Georgia, Florida and Louisiana -- all bolt to the opposition camp, Bork's opponents would be within easy striking distance of the 51 votes needed to defeat the nomination on the Senate floor.

Some of these southern Democrats such as Sen. John B. Breaux of Louisiana have stopped just short of a formal announcement that they will vote against Bork. Moreover, several have suggested that the southern Democrats, seeking political cover on a highly visible and divisive issue, are likely to move in unison.

"I think everybody is looking at this through different glasses, but sometimes you see the same thing," said Sen. Richard C. Shelby (D-Ala.), who, like Breaux, is a freshman whom Reagan campaigned furiously against last year.

There was also widespread skepticism on Capitol Hill that Reagan, nearing the last year of his presidency, could do much to salvage the nomination. Unlike legislative battles, Breaux noted, a Supreme Court nomination "is not something you can trade on" or work out a carefully calibrated compromise.

"On this thing, it's up or down," he said. "I can't vote for Bork with amendments."

In addition, it was unclear how much influence Reagan will be able to bring to bear on Democrats he had campaigned against.

"If they call me and say win one for the Gipper {Reagan}," said Breaux, "it doesn't apply in the scenario. If the old Gipper had had his way, old Breaux wouldn't be here."

Sen. Howell Heflin (D-Ala.), a key undecided member of the Judiciary Committee who frequently votes with the administration, was summoned to the White House, apparently the first Democrat lobbied by Reagan since the nomination. In a 15-minute meeting, Reagan hinted no disillusionment, according to Heflin.

"He was quite vigorous in his arm-twisting," Heflin told reporters.

The second-term senator said, however, that the session had not won him over, adding that he still has serious unresolved questions about Bork. He said Reagan told him nothing that he had not already heard from Bork's supporters, adding that the president concentrated on Bork's qualifications, and did not offer to trade legislative favors.

Would the arm-twisting ultimately affect his vote? "We'll have to wait and see," answered Heflin, who insisted he has yet to make up his mind.

Specter said he began leaning heavily against Bork in the second week of committee hearings but did not decide until Wednesday, when he held a third private meeting with the 60-year-old U.S. Court of Appeals judge and was lobbied a last time by Lloyd N. Cutler, White House counsel under President Jimmy Carter and a strong Bork supporter.

Specter said yesterday morning he called first Bork and then Baker at the White House to inform them of his decision.

Specter said he became convinced that Bork's controverisal views as a Yale Law School professor would continue to guide his thinking as a Supreme Court justice even though Bork disavowed some earlier stands and moderated others during his testimony before the Judiciary Committee.

"In the final analysis, if I retained substantial doubt as to what Judge Bork would do on fundamental questions of constitutional law, I thought my obligation was to vote no," Specter said.Staff writer Dale Russakoff contributed to this report.