President Reagan, like any accomplished politician, relies on some unlikely alliances to accomplish his purposes. This year he is counting on the Soviets and his own Blue Ribbon Commission on Defense Management to rescue his embattled military budget from Congress.

The White House game plan goes like this: Contend that the Soviets have returned to the nuclear arms bargaining table because of the Reagan defense buildup and the Strategic Defense Initiative. Point out that Soviet leader Mikhail Gorbachev is coming here for a second summit meeting. Argue that defense cuts would send a message of weakness to the Soviets and undermine prospects for a summit arms control agreement.

The president knows that Americans reject the view that the U.S. military establishment is starving. White House polls show that voters believe the Pentagon to be wasteful and inefficient. Congress is reacting skeptically to an administration budget that seeks $33 billion more for defense while cutting $23 billion in domestic programs.

The White House responded to the political problem last June by forming a commission to study Pentagon management and procurement policies and naming former deputy defense secretary David Packard as director. Somewhat defensively, Reagan said that a "public misconception" had developed about military wastefulness "born, at least in part, of a drumbeat of propaganda and demagoguery that denies the real accomplishments of these last four years."

White House strategists hope to use the findings of the Packard Commission to answer this "misconception." When the commission issues its first report Feb. 28, Reagan intends to make a show of implementing its recommendations. On Feb. 19, he intends to make a nationally televised speech on national security issues and express an interest in reforming the Pentagon as well as enriching it.

Reagan's latest defense budget is going to take some selling, even for a president who is a super-salesman. Reagan lost his best chance of reform early in his presidency when he threw money at the military while decrying "waste, fraud and abuse" in government domestic spending. Defense contractors were in hog heaven. They had more business than they had ever dreamed of in peacetime, with few restraints attached.

Part of the problem was Defense Secretary Caspar W. Weinberger, whom the president's aides naively expected to live up to the sobriquet of "Cap the Knife," which he had earned while presiding over the budget office during the Nixon administration. But Weinberger's bureaucratic clients in the Defense Department were the military services, not federal budget-cutters, and he became in large measure their captive.

My colleague, military affairs reporter George C. Wilson, has compared Weinberger to a university president who focused on fund-raising and left management to the deans, in this case the various service secretaries. With the conspicuous exception of Navy Secretary John F. Lehman Jr., who built the Navy while keeping an eye on the dollars, the deans weren't up to the job.

Weinberger was not quite as oblivious to what was happening as some of his critics charge. His first deputy, veteran bureaucrat Frank Carlucci, proposed a series of management reforms likely to be echoed in the Packard Commission report. On programs where he personally exercised oversight, such as the B1 bomber, Weinberger appears to have been cost-conscious and effective. Overall, however, he succeeded as a fund-raiser and came up short as a manager.

Reagan came up short, too. When he arrived at the White House, he could have had the MX missile for the asking, but he was unwilling to accept a basing system approved by his predecessor Jimmy Carter. Reagan raised the consciousness of Americans about the needs of a military that been on short rations since the Vietnam war, but he failed to define or limit those needs.

Now he has to do the hard way what he might have been done easily five years ago. Administration officials are hoping that Gorbachev and the Packard Commission won't let them down.

Reaganism of the Week: Speaking at a prayer breakfast on his birthday, the president said: "Seventy-five years ago, I was born in Tampico, Ill., in a little flat above the bank building. We didn't have any other contact with the bank than that. Now here I am, sort of living above the store again."