As the White House senior staff wrestles with legislative strategy for 1983, a campaign declaration of former independent presidential candidate John B. Anderson is haunting the Reagan administration.

When Anderson was still a Republican, in the historic debate of GOP presidential candidates in Iowa on Jan. 5, 1980, he asserted that there was only one way that Ronald Reagan would be able to accomplish his multiple promises of increasing military spending, reducing taxes and balancing the federal budget. "It's very simple," said Anderson. "You do it with mirrors."

An administration official recalled his comment last week during an apprehensive discussion of the budget difficulties ahead. Talk of a balanced budget during Reagan's term has, of course, long ago been abandoned. Administration officials also conceded last week that there is almost no chance of prying the balanced budget constitutional amendment out of Congress next year, although Reagan probably will make a grandstand play in its behalf.

The president's Economic Advisory Board has suggested to Reagan that he show his dedication to the concept by submitting budget projections which show steadily declining deficits culminating in a balanced budget by 1987. But Reagan's unyielding commitment to military spending and his opposition to any tax increases make such projections unlikely, unless they are accomplished through use of those proverbial mirrors.

On the immediate issue of producing a credible budget next year, the problems seem even more formidable. The president will plunge into budget discussions this week, at a series of meetings with senior aides and economic officials, but the forecast for fiscal 1984 is for a deficit exceeding $175 billion, even with some additional cuts in domestic spending.

Last year the White House senior staff fought successfully to turn Reagan around and obtain some tax increases and reforms. But the fire is gone from the belly of these officials now and they are depending on Congress, especially the GOP-controlled Senate, to do their work for them.

"What does the president say when it is pointed out to him that some defense cuts are necessary to get the deficit down?" a reporter asked last week.

"He says that we went for tax increases in October and now is the time to go for defense increases," was the reply.

Two high ranking administration officials are perceived as posing particular difficulties in the budget process, but for vastly different reasons.

Budget Director David A. Stockman is what one White House source calls "a historic obstacle" because of the loss of credibility he suffered last year when he revealed the creative nature of the administration's economic assumptions. This time Stockman is expected to be highly realistic about the budget and the amount of the deficit it will produce.

The present and more serious obstacle, in the view of many administration officials, is Secretary of Defense Caspar W. Weinberger. Unlike several other Cabinet members, Weinberger is universally viewed as bright, dedicated, hard working and effective. But he also is seen as rigid and uncompromising and, by some, as a captive of the Pentagon brass.

"We'd be far better off on the defense budget in the long run if Cap would back off a little now and recognize that a huge deficit is more of an immediate menace than the Russians," said one administration insider. "Cap could convince the president, too. But we can't convince Cap."

Deputy chief of staff Michael K. Deaver and presidential assistant Richard G. Darman return tonight from a four-day South American trip, the first of two such trips which will advance Reagan's five-day journey to Brazil, Colombia and Costa Rica, beginning Nov. 30.

The president will be absent during the first week of the lame-duck session of Congress, an absence which accurately reflects the administration's low expectations for the session . . . Vice President George Bush meanwhile will begin a two-week, seven-country trip to Africa on Nov. 10, accompanied by an official party of 14.

California Gov. Edmund G. (Jerry) Brown Jr., defeated in his bid for a U.S. Senate seat, has a reputation in many quarters for being a cold fish. But you couldn't prove it by Reagan administration political adviser Ed Rollins, who received three messages from Brown last week while Rollins was recuperating from a stroke at George Washington University Hospital.

"Hang in there," Brown said in one telegram. "I'm going to win without you. Don't cop out on me now. This will teach you to work against my candidacy. Sincerely, get well soon." . . . Sen. Bob Dole also did his bit. He sent Rollins an intravenous bottle inscribed with the M*A*S*H insignia, thoughtfully filled with vodka.