It may have been "a quiet week in Lake Wobegon," as the Bard of St. Paul says, but it has been a rotten winter for one of Garrison Keillor's fans, Rudy Perpich, who is finishing his first full term as Minnesota's governor.

Last year, with Minnesota outpacing its neighboring states in economic growth, Perpich signed a major tax cut designed to improve the business climate. But with farm income continuing to collapse and the computer peripheral companies in trouble, he now faces what may be a $500 million revenue shortfall.

Both praised and criticized for his frequent overseas "trade development" missions, the man Republicans label "Wandering Rudy" appparently stepped over the line when he went to Austria before Christmas to check out some castles as possible sites for a University of Minnesota European center. The outcry was such that he has grounded himself.

And then came the bitter Hormel packing- company strike in Austin and the decision by the Democratic Farmer-Labor (DFL) governor to send in the National Guard. Now the doorway to the governor's office is flanked by hand- painted signs reading: "We didn't elect you to break strikes" and "Workers can't negotiate at gunpoint." Perpich, whose father was a miner on the Iron Range, has ordered that the union protests not be removed. "It's hard," he said, "but I've been where they are."

As if that were not enough, it has gradually become clear to Perpich and the rest of the Minnesota political community that St. Paul's second-most-powerful political figure, Mayor George Latimer, is dead serious about challenging his fellow-Democrat's ambition for another term.

It is a showdown the DFL dreads. These are two strong-willed men, and their collision could be bloody. Perpich is a moody giant from a family of hard-knuckled politicians. He was elevated from lieutenant governor into the governorship in 1977 in a deal that saw Gov. Wendell Anderson resign to accept appointment by Perpich to the Senate vacancy created by Walter F. Mondale's election as vice president.

In 1978, Minnesota voters showed how little they liked that finagling by defeating both Anderson and Perpich. But in 1982, Perpich rebounded, defeating the party-endorsed Mondale prot,eg,e, Warren Spannaus, for nomination, and beating a weak Republican in November. Though not a polished public figure, Perpich has pushed through some significant education and economic measures this term and even Latimer concedes "has done far more good than harm."

Latimer is something else -- a bearded, bouncy lawyer who in the past decade has transformed St. Paul from being Minneapolis' overlooked little brother into a national model of downtown and neighborhood revitalization and energy, conservation and economic development innovation. As the recently retired president of the League of Cities, he has become a national spokesman on urban policies.

If you ask why he is running for governor without any fundamental disagreements with Perpich, Latimer says, "I kid myself that I'm the hormonal candidate. But honestly I'm more fired by the sense of the possible at age 50 than I was at 30 or 40. This 50th year has been terrific: Our kids are all in good shape; I just won reelection with 85 percent of the vote after 10 turbulent years; and I really believe this state is at a critical juncture where its future depends very much on the vision of its leadership."

After standing aside for the leadership-endorsed Spannaus in 1982, and watching Perpich trounce him in a primary, Latimer is understandably not moved by the argument that Perpich has the "right" to be uncontested. He is scornful of those in the DFL leadership who have rushed to embrace Perpich after quarreling with him for most of the last four years. "I say, listen, you turkeys, don't tell me to revere a system (of endorsement) you have corrupted."

While officially keeping his options open, Latimer makes it plain that "it would be pretty dumb to challenge an incumbent who is fairly popular" for endorsement at the DFL convention. "As a snarky guy," he has hinted occasionally at running as an independent in November -- a path that Perpich and others think would almost certainly guarantee a Republican victory. "But there really is a question of governance and continuity if you go that way," Latimer says.

So the prospect is that he and Perpich will meet in the September DFL primary. Perpich says that does not worry him, since his home territory in northeastern Minnesota regularly turns in huge majorities for local heroes opposing Twin Cities politicians. "There's no way he can win a primary," the governor says.

But the Minnesota Poll of the Minneapolis Star and Tribune in December showed Latimer known to more than four out of five voters and viewed favorably by 71 percent of them, making him "a formidable opponent."

With three acknowledgedly weak candidates now in the field, Republicans are scrambling to find someone who may be able to exploit the opportunity. And in Mondale's home state, the only state he carried in 1984, the Democrats are once again lining up in their favorite formation: the firing squad is in a circle.