The Republican National Committee, in a surprise move, yesterday unanimously endorsed the reelection of President Reagan and Vice President Bush, and, as expected, installed Sen. Paul Laxalt of Nevada as the party's first general chairman.

Contributing to what is becoming a drumbeat of pressure on Reagan to run for reelection, Laxalt, Reagan's closest adviser in Congress, told the committee that he doesn't think Reagan "has any real choice" except to run.

"In terms of the the political consequences, in terms of the mission, we can't get the job done in four years," Laxalt said. "I hope when the day of reckoning comes that he'll declare himself a candidate. And I think he will."

The surprise move to endorse Reagan and Bush, cutting off would-be GOP rivals, came at the suggestion of former Ohio governor James Rhodes, one of the party's senior leaders. He said he decided to offer the resolution because he didn't want the president "to be hindered by bickering, would-be candidates waiting in the wings."

Laxalt, a second-term senator, was elected unamimously. In a nominating speech, outgoing Transportation Secretary Drew Lewis said Laxalt's first mission should be "to go down to the White House and demand that Ronald Reagan run for reelection."

Laxalt, 60, has been close to Reagan since both served as governors, and he was Reagan's campaign chairman in 1976 and 1980. His new post, created for him, represents an unusual centralization of political power.

It is designed to make Laxalt overseer of three party committees--the Republican National Committee and GOP House and Senate campaign committees--as well as the White House political office and Reagan's reelection effort if he decides to seek a second term.

Laxalt will not be the national committee's chief operating executive. His protege, Nevada state GOP Chairman Frank J. Fahrenkopf Jr., 43, a Reno attorney, will fill that role. Fahrenkopf was elected RNC chairman unanimously, succeeding Richard N. Richards, who resigned after two tumultuous years.

In an acceptance speech, Laxalt vowed that the new arrangement will lead to party unity and will not diminish the role of the national committee, which he called "the most potent political organization in the country," or the House and Senate campaign committees.

"As far as I'm concerned, there'll be no turf battles," he said, adding that the key to the success of Republican candidates at all levels depends on the election of a Republican president in 1984.

Laxalt told a cheering audience he agreed to take the job only after becoming convinced in "an eyeball-to-eyeball" conversation with Reagan that he "will very definitely be a candidate for reelection."

"And I hope George Bush is going to be his running mate," Laxalt added. "He's done a great job."

But in his speech and in an interview later it was clear that Reagan has not given Laxalt any firm pledge about his future plans.

Fahrenkopf, accepting election, told the committee, "The future has never looked so bright for our party and our nation." He pledged to work to involve more women and blacks, who have not been identified with the party.

He retained other principal officers of the committee. They include party co-Chairman Betty Heitman of Louisiana, Treasurer William J. McManus of Washington, Finance Chairman Mike Curb of California, and Deputy Chairmen Frederick K. Biebel of Connecticut and Rich Bond, a former Bush political operative.