Conservative and liberal groups are preparing for a multimillion-dollar lobbying battle over the Supreme Court nomination of U.S. Appeals Court Judge Robert H. Bork, with efforts already under way by both sides to organize grass-roots support in key senators' states.

Almost as soon as Bork's nomination was announced last week, both sides started to write and telephone their members, recruit other groups, bombard editorial writers with information about the Senate's role in the confirmation process and design advertising campaigns and legislative strategies to prevent or assure Bork's elevation to the high court.

At the annual convention of the NAACP in New York yesterday, delegates unanimously passed a resolution criticizing Bork's stands on public accommodations laws, the death penalty and affirmative action and calling for an "all-out effort to block" Bork's confirmation.

"We must let our senators know that a vote against Mr. Bork is a prerequisite for our vote in the next election," Coretta Scott King, widow of the Rev. Martin Luther King Jr., said to loud applause.

NAACP Executive Director Benjamin L. Hooks, who vowed on Sunday that the civil rights group would fight Bork's nomination "until hell freezes over," said yesterday that the group is organizing a letter-writing campaign and will appeal to other civil rights organizations to speak out against Bork's nomination.

"I don't want to get focused on the narrow issue of pro-choice {on abortion}," Hooks said in an interview. "That's important . . . but there are other issues that deserve to come to the front."

The 1.8 million-member National Education Association, the nation's largest teachers union, also voted at its convention Sunday to fight the Bork nomination. The National Organization for Women and the National Abortion Rights Action League will both concentrate on the fight against Bork at their annual meetings later this month.

NOW President Eleanor Smeal said the group plans to organize rallies against Bork, establish telephone banks to generate mail and telegrams to key senators and set up a computer bulletin board to keep its 150,000 members informed about the status of the nomination.

People for the American Way, a liberal lobbying group founded by television producer Norman Lear, has five or six people working full time on the Bork nomination and about $360,000 in "seed money" to spend on the battle against confirmation. "We're talking at least a million on this campaign," said Executive Director Art Kropp.

He said the group will send an "alert mailing" to its 250,000 members today "to get them prepared" for the battle, and will organize members to telephone key senators when the nomination comes before the Judiciary Committee.

"We're talking about a heavy newspaper print-ad strategy and radio strategy, hoping to reach saturation in some of the markets," Kropp said, with advertising heaviest in the "opinion-making markets" of Washington, Chicago, New York, Los Angeles and Atlanta.

"We want the American public to be speaking with anyone who might be wavering," Kropp said. "We view it as being probably the most important thing we do this year."

Likewise, conservative groups have weighed in for what direct-mail expert Richard Viguerie described as "the biggest liberal-conservative battle since the 1984 election."

"It began immediately. The first meetings of conservative leaders to brainstorm and begin to start action were the very next morning," said Patrick McGuigan of Coalitions for America, a conservative lobbying umbrella group.

Concerned Women for America, a 500,000-member conservative group, sent letters yesterday to about 50 "area leaders" nationwide asking them to activate "phone banks" to urge members to write their senators in support of the nomination. "We're alerting our membership. We're very thrilled about the Bork nomination," said spokeswoman Rebecca Hagelin.

The American Conservative Union sent its top 1,000 contributors what Executive Director Dan Casey described as a "here-we-go-again letter," asking them to send contributions to support the Bork effort and to urge their senators to back Bork. Casey said the group would send another 40,000 to 60,000 letters to supporters by the end of the month.

"We're going to go all out," Casey said. "This is an issue that will fund itself because it's what they would say in the direct-mail world is a 'hot-button' issue. Frankly, the liberals have made this a hot-button issue for conservatives . . . with the absolute incredible reaction," he added. "Every dollar that Norman Lear spends is probably more support for Judge Bork."

Representatives of the National Conservative Political Action Committee (NCPAC) and the Conservative Caucus said they are also planning heavy direct-mail drives to support Bork.

Meanwhile, both sides are battling for the hearts and minds of the nation's editorial writers, and through them, the American people.

People for the American Way and the Alliance for Justice last week sent mailings to 1,700 newspaper editorial writers stressing the importance of the Senate's "advice and consent" role in considering nominations.

The conservative Coalitions for America and the American Conservative Union counterattacked yesterday with a packet of materials emphasizing the limited role ideological considerations should play.

"You can surmise that whatever the liberals have, we're going to have -- radio, television, newspaper ads," Viguerie said.

Bork supporters and opponents agree on the importance of mobilizing grass-roots support for their cause from voters who can contact their senators and express their views on Bork.

"There's no question that the mobilization of the grass roots is one of our most critical tasks," said Ralph Neas of the Leadership Conference on Civil Rights. "Senators have got to hear from their own constituents. It's one thing to have good Washington representation, but you first and foremost need to have the constituents of the senator contact the senator."

"There's only so much you can do out of Washington," said Casey of the American Conservative Union.

In that effort, both groups will be focusing on the same middle group of senators -- first the swing votes on the Judiciary Committee, primarily Dennis DeConcini (D-Ariz.), Howell Heflin (D-Ala.) and Arlen Specter (R-Pa.), and later the Southern Democrats and moderate Republicans whose votes will be crucial in the full Senate.

"I've talked with many of my friends who are in leadership positions in the various conservative organizations," said McGuigan of Coalitions for America. "I'm telling them to roll out the mail immediately to their grass roots asking their grass roots to communicate with the targeted senators, and I have the same target list as the left."