President Reagan, faced with surveys that show public opinion turning against Judge Robert H. Bork, will attempt to rescue his embattled Supreme Court nomination with an intense, personal lobbying effort directed at undecided senators, administration officials said yesterday.

"What happens now is hand-to-hand combat," said White House political adviser Frank Donatelli. "The outcome will be very close, and it's up for grabs."

Reagan advisers said the president has rejected any "backup strategy" for an alternative to Bork and plans to begin making telephone calls to key senators and holding one-on-one meetings with some of them. A senior official said Reagan had made Bork his "No. 1 domestic priority" and would call for his confirmation in virtually every public appearance.

Meanwhile, Senate Majority Leader Robert C. Byrd (D-W.Va.) told NBC News that he had recommended to Senate Judiciary Committee Chairman Joseph R. Biden Jr. (D-Del.) that the Bork nomination be sent to the Senate floor without a recommendation, a move that would allow undecided senators to delay a decision and give both sides more time to maneuver.

As the committee began its third week of public hearings on the nomination yesterday, Biden announced that its vote on Bork, originally set for Thursday, would be put off until next week. He said the hearings would end this week, possibly as early as Wednesday.

Strategists for both sides acknowledge that the fate of the nomination is up in the air, with 20 or more senators undecided. But there is also a clear sense among pro-Bork forces that they have been thrown on the defensive by an effective public relations campaign by Bork's opponents.

Senior officials said that a survey taken for the White House produced a similar result to last week's Washington Post-ABC News poll, which showed that a slight plurality of those aware of the nomination opposed Bork. Both surveys found voters shifting from undecided to a position of opposition.

"There's no question that the public relations war heated up and we didn't do well," said one strategist. "We got killed. The civil rights groups turned it into a political campaign. Look at the polls. They've scored some points, indeed."

This source also complained about the inactivity of conservative groups in the public battle. When Bork was nominated, he acknowledged, the White House told right-wing groups to "calm down" for fear they would play into the hands of Bork's opponents, who have tried to portray him as a right-wing zealot. But, he said, "they've calmed down to the point they've gone underground."

A number of the conservatives complained, however, that the White House miscalculated by underestimating the intensity of the assault on Bork.

"They came to the realization too late that this was going to be trench warfare," said Daniel Casey, executive director of the American Conservative Union. "They failed to shift gears in time and recognize the need to get the president more frequently out front."

"The White House was figuring out that this was a real fight in September," said Patrick McGuigan, legal affairs analyst for Coalitions for America, a conservative umbrella group. "We figured out it was a real fight in July."

McGuigan said the White House rebuffed suggestions for an "August offensive" on Bork's behalf, instead limiting Reagan's effort during his California vacation to a single meeting with law enforcement groups.

"That was the August offensive," McGuigan said. "It was a joke for that to be the whole thing."

White House officials pointed out that Reagan emphasized Bork's confirmation in three of the five speeches he made on his vacation, two of them in Nebraska en route to his California ranch. They also disputed conservative complaints that the White House had erred in presenting Bork as a mainstream candidate, instead of an ardent conservative.

"First of all, the president considers Bork to be centrist and a strict constructionist, which is the way we've been presenting him," said one strategist. "It never works for this president when the presentation isn't close to what he thinks about things. Secondly, we would not have had the support of people like {former chief justice} Warren Burger and {former president} Gerald Ford if we had offered Bork as a right-winger."

White House officials now hope that conservative supporters will stop second-guessing early strategy and help in the confirmation fight.

"There's no one at the White House with a defeatist attitude," said White House communications director Thomas Griscom. Legislative strategist Will Ball said the outcome is "truly an open question" that could be decided by the president's participation.

"Since the nomination the president has been speaking out publicly," Ball said. "He will continue to do so, but he will also turn his attention to getting votes in the Senate."

Reagan is scheduled to keep up his public campaign for Bork today at the signing of a deficit-reduction bill and continue it Wednesday at a meeting of Bork supporters and Thursday at the swearing-in of new FBI Director William S. Sessions, where the president will emphasize Bork's position on criminal justice issues.

Reagan's higher profile in the confirmation fight was signaled by Assistant Attorney General John R. Bolton, who has been coordinating the administration effort at the Bork hearings.

"The president's speech on Friday was a harbinger of what is to come," Bolton said. "This is, after all, a presidential nomination and he cares about it . . . . Overall, as the hearings conclude and we move into the next stage, both the president and the administration as a whole will be much more visible." Reagan on Friday told a group of conservative women that Bork's critics are "ideologically inspired" and predicted that the 60-year-old appeals court judge would be confirmed.

Bolton denied the growing impression that the Bork nomination is in jeopardy because of the constant pounding by opponents during the hearings.

"I don't think the tide is running in either direction," he said. "Because the vote is not immediately in sight, there are a lot of genuinely undecided senators."

The administration may be playing for time, as Reagan begins to launch his counteroffensive. During the summer, Republicans complained bitterly about the mid-September start of hearings, accusing Biden and the Democrats of attempting to kill the nomination through delays. There were no complaints yesterday from Judiciary Committee Republicans when Biden announced the committee vote would be put off until next week.

Byrd said in his interview with NBC News that he did not see how the vote on the nomination could be set before Nov. 2 "at the earliest."

Bork's supporters are eager to have the committee hearings end. Senate Minority Whip Alan K. Simpson (R-Wyo.), a member of the committee, said the committee is so polarized that the issue will not come into focus until it reaches the Senate floor.

"For me, . . . {the hearings} have been a steady drumbeat of the anti-Bork campaign," he said. "That's not going to change until we get it to the floor . . .Then we will get a whole new sense of balance."Staff writer Ruth Marcus and staff researcher Michelle Hall contributed to this report.