A scramble is on in Washington as various factions push their favorite candidates as the successor to Edwin Meese III as U.S. attorney general. Yet it may not be possible to have another full-fledged attorney general in the few months remaining in the Reagan administration.

In fact, there is a chance that Salt Lake lawyer Harold Christensen, recently nominated as deputy attorney general, the No. 2 post in the Justice Department, could finish up the year as acting attorney general.Meese said the qualities needed as attorney general are loyalty to the president, integrity, and dedication to the law. Christensen easily qualifies on all those counts.

Among the names being mentioned to replace Meese are, former White House chief of staff Howard Baker; Solicitor General Charles Fried; Interior Secretary Donald Hodel; lobbyist and former senator, Paul Laxalt of Nevada; Gov. James Thompson of Illinois; Howard T. Markey, chief judge of the U.S. Court of Appeals; Judith Richard Hope, a nominee for the U.S. Court of Appeals in Washington; Eugene Thomas of Idaho, a former president of the American Bar Association, Rudolph Giuliani, U.S. attorney in Manhatten; former Pennsylvania governor Dick Thornburgh; and, of course, Christensen.

Some of these people might not be willing to give up current situations for an uncertain post that could last only a few months, if confirmation is possible at all. But there is one thing that could make the job more attractive. Vice President George Bush says that if he wins the presidency, he would "not rule out" having the new attorney general stay on in his administration.

However, there are very real problems with time. Meese will be on the job until the end of July or early August, leaving only five months in the Reagan presidency. Congress will be in session for less than four months. A nominee would have to be found, his name submitted to the Senate, and approval given by that Democratic-controlled body, all before Congress adjourns to go home and campaign prior to the November election.

In addition, Congress will recess as the Democrats hold their national convention in late July and the Republicans do likewise in mid-August. The opportunity for serious business will be very, very brief.

Of course, Congress could - and should - act quickly if an acceptable nominee were produced in short order. Yet experience has shown that is not usually the case. And this year has a lot of distractions.

Even for Christensen, in line for a less-than-Cabinet-rank job, the process has been slow. He was picked for the No. 2 post by President Reagan in late May and doesn't have a confirmation hearing with the Senate Judiciary Committee until July 28 - nearly two months later. He has been on the job in an unofficial capacity for several weeks.

One of the problems facing Christensen is that he has been officially nominated for the No. 2 job and his name is being suggested for the No. 1 post in the department. Clearly, he can't be both. But he has some advantages, too.

Since the confirmation process already has been set up in his case, it would make sense to nominate Christensen as attorney general. Barring that, he could proceed with confirmation in the No. 2 job and serve as acting attorney general until the end of the year.