WASHINGTON (AP) _ For very different reasons, George Bush and comedian Jay Leno want Dan Quayle on the 1992 Republican ticket.

When Bush praised Quayle as ''an outstanding vice president'' who has his heart in his job, late night television personality Leno quipped, ''Now if he can just get his mind in the job.''

Eleven months after the former Indiana senator survived a difficult political campaign and became vice president, he has Bush's support for another four-year term.

At the same time, though, he remains a popular target for the likes of Leno - and a worrisome factor for Republicans watching public opinion polls giving Quayle consistently low ratings.

''I'm not going to do anything differently no matter what the polls say,'' Quayle recently told reporters. ''I'm going to work as I believe a vice president should work, that is, first and foremost with complete loyalty to the president, for the advancement of his agenda, in his interests and that's what I'm doing.''

The most recent surveys, a Wall Street Journal-NBC News sampling taken early this month, reported more than half of the voters said Bush should choose a different running mate in 1992. Quayle could not even claim support from the Republicans polled. By a 40 to 39 percent margin, they said he should be dumped.

''You can't argue with those polls. It's unfortunate that people haven't recognized his contributions to the administration and the party,'' said Quayle's press secretary, David Beckwith.

He said Quayle has accomplished his first-year goals of solidifying his position within the White House and with Bush and of working with Republican Party officials around the country.

''As people begin to recognize his contributions in those areas, the polls will take care of themselves,'' Beckwith said.

The vice president also has emerged as a link with the White House for conservatives, some of whom are distrustful of Bush. And Quayle is credited with raising $5 million in campaign contributions for GOP candidates and causes.

Expectations were low when Quayle took office, in part because of a presidential campaign in which his selection became an issue.

Even now, praise for the vice president from Republicans often begins with a sigh of relief that Quayle has avoided serious gaffes and avoided embarrassing the president.

''He's fulfilling the functions for which he was selected,'' said political analyst William Schneider of the American Enterprise Institute. ''He does not challenge, he does not question the president. He doesn't make any trouble.''

His standing wasn't helped by a new book on the 1988 campaign, ''Whose Broad Stripes and Bright Stars'' by reporters Jack Germond and Jules Witcover. Republican consultants who worked with Quayle in the campaign were quoted as offering unflattering descriptions of the vice presidential nominee.

''He was like a kid,'' the book quoted Joseph Canzeri as saying. ''Ask him to turn off a light and by the time he gets to the switch, he's forgotten what he went for.''

When asked by Dallas Morning News reporters this month whether he would keep Quayle on the ticket, Bush seized the chance to say he ''absolutely'' would.

That word from Bush - a vice president himself for eight years - was widely regarded as a move to head off rumors that were beginning to surface regarding Quayle's future.

''Bush knew better than anyone else how frustrating such rumors are and wanted to put them to rest,'' said an administration official who spoke only on condition of anonymity.

Given Bush's support for his vice president, Republicans were insistent that they not be linked by name to any critical statements. One party official said GOP stalwarts ''are trying to make the best of what might otherwise be a bad situation.''

In speeches, Quayle often puts his own stamp on administration policy, careful to follow Bush's lead but adding a conservative edge.

Quayle is a passionate defender of the Strategic Defense Initiative - the space-based missile defense system - and he takes a consistently skeptical view of the Soviet Union's reform moves.

Recently he took a harder line on U.S.-Soviet relations than the more optimistic view articulated just a day earlier in a major speech by Secretary of State James A. Baker III. The White House hastened to insist that the two speeches were not inconsistent.

Despite private grumbling within the GOP, there is no shortage of Republicans willing to praise Quayle publicly.

''Dan is personally well liked. He is eager to help everyone on both a partisan and non-partisan level and he has the support of the president,'' said Rep. Lynn Martin, R-Ill., a close ally of Bush.

On the fund-raising circuit, the Republican National Committee touts Quayle as one of its principle assets - with some $5 million to his credit so far. RNC spokeswoman Leslie Goodman said Quayle has been adept at building support among party regulars at the state and local level.

New Jersey Gov. Thomas Kean said Bush ''is absolutely convinced that Dan Quayle is a good public servant and that he is growing and that he is learning on the job.''

''He needed that kind of reassurance from the president,'' said Kean. Rumors that some factions wanted to dump Quayle from the ticket in 1992 were ''very, very destructive,'' when the vice president travels as a representative of the administration, Kean said.