THE REPUBLICAN Party faces an important test this week. It must put together a plan for dealing with the very large budget deficits that threaten the country's economic future. The plan must be more than a public relations exercise, an excuse for shifting blame to political rivals or predecessors. It needs to be understandable by and acceptable to most of the public. And it must be fair to and careful of those people least likely to be able to protect themselves. That's a huge order. But it is not too much to ask of a party that wants to be -- and is well on its way to being -- the country's dominant political force for years to come.

The Republican Party has been in control of the White House for 12 of the last 16 years, but it has only controlled the Senate during the four years of the Reagan presidency. Only in 1981, its first year in office, did the Reagan administration exert major influence on economic policy. That was when the president pushed through Congress the combination of big tax cuts, major defense spending increases and smaller domestic budget cuts that produced the enormous budget deficits that the country has experienced ever since.

Enacting the 1981 economic program required strong presidential leadership, but it didn't really call for much political courage. The sacrifices it required -- social program cuts -- were focused on lower-income people with little political power, while the benefits it offered -- lower taxes and defense jobs -- were broadly popular.

Since that time the administration has obstructed as much as it has led efforts to cope with the unwanted, but not unforeseen, consequences of its 1981 policies. Deficit-reducing legislation -- the tax reforms of 1982 and 1984, the Social Security reform package, additional domestic budget cuts and some slowing of the military buildup -- has been fashioned by Senate and, occasionally, House leaders, passed with bipartisan cooperation and grudgingly accepted by the White House.

That strategy of hanging back while Congress acted has provided convenient political cover for President Reagan, enabling him to take credit for progress while distancing himself from the unpleasant side effects. But it has produced only minor accomplishments -- by and large just enough savings to offset mounting interest costs of the mammoth debt, but not enough to shrink the annual deficit.

Now Congress needs to do more than simply run hard to stay in place. The rebound from the deep recession of 1982 seems to have petered out. The economy is straining to accommodate both record- breaking budget deficits and, partly as a consequence, enormous trade deficits. The budget compromise reached between the White House and Republican leaders would make a convincing start toward narrowing future deficits. But it is not a fair and workable plan -- too much is asked of the old and needy, too little is asked of well-off taxpayers and the military. Devising an acceptable, but still ambitious plan will require standing up to some tough lobbies and dealing in good faith with political opponents. Can the governing GOP do it?