UNLESS WILLIAM J. CASEY and James A. Baker III decide to settle their differences with pistols on the Mall at dawn, their unhappy chief is going to have to choose between them.

It is not an easy matter to decide between your White House chief of staff and your CIA director, and Ronald Reagan is understandably flinching from the task of selecting the one who is "mistaken" about who gave the Carter debate papers to whom in the fall of 1980.

There was a time when Reagan could have avoided that cruel choice.

He could have, when the suspect list was short -- Casey, Baker, OMB Director David Stockman and Communications Director David Gergen -- summoned them to the Oval Office, asked who got what from whom and arrived right at "the bottom of it," which is where he says he wants to go.

Answers in hand, he could have escorted the Big Four to the presidential woodshed, administered a ritual belting for something like "excessive zeal" and insured that the tale would become the "one-day wonder" of his people's claims.

But he didn't. He left the impression that he doesn't want to know. He also left himself open to the shower of little acid raindrops which keep falling on his head, as more recipients of "pilfered documents" are flushed out, and the cast of characters grows by the day.

Of course, it is not his style to play detective. One of the secrets of his great success is that he is not, as his predecessor was, "a micromanager." He does not read the fine print. He's a broad-brush man.

He may also sincerely believe that it was "much ado about nothing." His standard with other appointees caught in eyebrow raising conduct, has been, "If it is not illegal, don't worry about it." By bundling the matter over to the Justice Department, he thinks he has finessed the ethical question, which he tried to dismiss at his hapless "heh-heh" press conference of June 28.

He may be counting on the seemingly bottomless reservoir of public good will he can always dip into when events dictate. The American people have tolerated much from Reagan -- high unemployment, a tilt to the rich, a laggard arms control policy, a nasty little secret war in Central America -- and he must have thought that campaign peccadilloes, presented as such, would be overlooked in the larger good of retiring Jimmy Carter from public life, a happening that was welcomed, even by that most partisan of Democrats, House Speaker Tip O'Neill.

The "politics as usual" line peddled by White House spokesman Larry Speakes initially sold well, as former Carter aides plied Capitol Hill with their wonted luck. Nobody wanted to hear that Carter was a victim of foul play, not even the avid press corps.

It wasn't even, for a while, "a Washington story."

Now it is much more than a Washington story. It never really was, unless you believe that interest in the character of the men who run the country is, and should be, limited to the harpies of the Capitol City.

One thing has led to another, and last Wednesday, spokesman Speakes' blow-dried cool wilted in the heat of the questions that have proliferated since the Big Four sent their stunningly defensive and contradictory replies to a letter of inquiry from Rep. Don Albosta, chairman of a Post Ooffice subcommitte known as the Committee on Human Resources.

Speakes stated with a straight face that there is "no conflict" between Baker, who says he got the stuff from Casey, and Casey, who says he never saw it.

Reagan is too political an animal not to know that his most precious political possession, his "nice guy" image, is in peril: nice guys don't take cribs into the final exams. Saying now, as his aides do, that he didn't really need the contraband, doesn't help.

If, in fact, they made no difference in Cleveland in 1980, they have already altered the shape of his next campaign, and possibly, the rest of his first term.

Baker, who was harpooned by Casey in an interview with The New York Times, is central to both. He may have to be benched in 1984.

The right wing, to whom he is the enemy of good things like the school prayer amendment, is already licking its chops over the prospect that he will have to walk the plank sooner. The moral indignation which eluded them during the Watergate matter trips off their tongues today.

Reagan is faced with the biggest public relations challenge of his political career. The other morning on the "Today" show, GOP super-flack Robert Keith Gray -- he had been identified as the recipient of campaign memo with "Report from White House Mole" written across the top -- was asked how the White House was doing in the PR sense.

Gray paused, finally said, "They underplayed it at the beginning. Now they are overplaying it."

Translation: It's out of control.