Senate Democrats say they elected George Mitchell as majority leader to give them an eloquent spokesman. Republicans like him, too - both as someone to work with and as a liberal to attack.

"I think it's a very good choice. George is very liberal, and it will push the Senate to the left," said Sen. Orrin Hatch, R-Utah, a conservative. "Whoever won that race was destined to be the spokesman for the Democrats in America.""It seems to me the Democrats have decided to move toward the left wing of the party and decided to do so with considerable momentum," said Richard Lugar, R-Ind. "This could make it easier for Bob Dole, as our leader, to obtain majorities.

"They are swimming against the tide of national politics," he said.

Mitchell, 55, of Maine, was elected Tuesday by the Democrats of the next Senate, handily defeating rivals Daniel Inouye of Hawaii and Bennett Johnston of Louisiana. Mitchell won 27 votes on the first ballot, compared with only 14 each for the others, and he then was declared the winner by acclamation.

The former federal judge and prosecutor emerged from the secret meeting and sounded a tone of caution and compromise, declaring that the Democrats would develop an agenda and "wait with interest and enthusiasm for the proposals of the next administration."

"We hope to move forward on a broad range of issues," he said, citing the federal deficit, health care, day care and the environment.

Mitchell planned to meet Wednesdaywith Senate Republican leader Bob Dole, R-Kan., a colleague from the Senate Finance Committee who was re-elected to his post by GOP colleagues on Tuesday.

"I'll be able to work with George Mitchell," said Dole, "He is a very bright, able and articulate senator."

Mitchell received congratulatory telephone calls Tuesday from President Reagan, President-elect George Bush, and Sen. Dan Quayle, R-Ind., the vice-president elect. Mitchell and Bush discussed plans to meet soon.

As majority leader, Mitchell is in charge of the legislative schedule, a power that will put him at the center of every important issue. He'll bring to the role a far different style from that of the man he's succeeding, Robert C. Byrd, D-W.Va.

Byrd, the Democrats' leader for the past decade, is known for his intricate, behind-the-scenes legislative maneuvering. Mitchell is a relative newcomer to the Senate - he was first appointed in 1980 - and is more comfortable on television and in public debate.

His voting record received an 85 percent rating from the liberal Americans for Democratic Action, compared to a 14 from the American Conservative Union.

Mitchell's opponents followed Senate courtesy after the election, praising and defending the new leader.

He will be "a great spokesman" who will put a personal stamp on the Senate and help the party, predicted Sen. Harry Reid, D-Nev., who had supported Inouye.