Secretary of State Alexander M. Haig Jr.'s resignation dashed President Reagan's hope of muddling through the 1982 elections without a Cabinet shake-up. Now, key White House advisers hope that Reagan can shuck another political liability and quickly dispose of Labor Secretary Raymond J. Donovan.

So far, however, the White House has received no sign that Donovan is willing to go quietly into the good night of political oblivion. And Reagan, who made no secret that Haig had overstrained his patience, has not indicated a readiness to jettison Donovan.

Short of an indictment, Reagan is most inclined to act decisively in a situation where his closest advisers are united, as they were in the Haig affair. The counsel on Donovan is divided. Among the key players, White House chief of staff James A. Baker III is considered the most "politically realistic"--that is, ready to dispose of Donovan when the time comes--and counselor Edwin Meese III is considered the most supportive of the embattled secretary of labor.

Haig's departure also has revived White House talk of changes to come after the congressional elections this November. The prevailing view is that Baker, who has said he will do whatever the president asks of him, will get a Cabinet post and that national security adviser William P. Clark, who earned his spurs as Reagan's executive secretary during the California governorship, will become White House chief of staff.

Deputy chief of staff Michael K. Deaver, the other key White House staff member, plans to leave at the end of the year even though the Reagans may ask him to stick around.

One concern that could affect this high-level lottery is the uncertain condition of Supreme Court Justice William H. Rehnquist, who recently underwent surgery of an undisclosed nature, reported by National Public Radio to be a hernia operation, at George Washington University Hospital.

Some administration sources speculate that the operation was more serious and that the 57-year-old Rehnquist could leave the court for health reasons. If this happened, the best bet is that he would be replaced by Attorney General William French (Pomme Frite) Smith, with Meese going to the Justice Department.

Meanwhile, in the real world, Charles Hagel, deputy administrator at the Veterans Administration, has submitted his resignation, focusing further attention on the many problems of the agency director, former California legislator Robert P. Nimmo.

There are administration officials of the see-no-evil, protect-all-cronies school who think that Nimmo's problems will disappear with the resignation of Hagel, a twice-wounded Vietnam veteran who tried in vain to make World War II veteran Nimmo focus on the problems of the Vietnam era vets. They are mistaken.

At least two veterans groups have met with Meese to urge replacement of Nimmo, who is under attack both for his undisputed love of perquisites (including a chauffeur and the building of a private shower) and for his purported foot-dragging on the budget for investigating the effects of Agent Orange, an allegation Nimmo has denied. Meese says the matter is under review, with a finding likely this week.

When is a long vacation not a vacation? In the White House view, it's when it becomes two vacations.

In the hopes of avoiding some of the criticism Reagan received last year for taking August off in California, the tactical thinkers at the White House have subdivided the 23 days the president was scheduled to spend in California during August this year into 12 days in July and 11 in August. It still adds up to 23.

Reagan's vacation, however, won't be as long as the gap between his last press conference, which was on May 28, and his next one, planned for early this week. It will end a span of enforced isolation that includes the European trip, when Reagan's opposite numbers among the leaders of the free world met freely with the press.

White House political aide Ed Rollins is pushing hard, with no evident success, for more black appointees and more use of current black appointees as Reagan spokesmen.

Rollins is reponding to pressure from black members of the administration, his own beliefs and the information from Republican pollster Richard Wirthlin that there are 50 congressional districts in the country where a 20 percent increase in the black vote could make the difference between victory and defeat for the GOP nominee.

The following dialogue occurred last week between a wire service reporter and a spokesman for national security adviser Clark.

The reporter called the spokesman after Haig resigned and wanted to know why. The spokesman said it was news to him that Haig had resigned.

The reporter then called Clark's office and asked to speak to the national security adviser. The secretary referred him back to the spokesman. "I'd prefer to speak to someone who knows that Haig has resigned," the reporter said.