Minnesota Republicans are exchanging some less than happy New Year's greetings.

The man who started the round of not-so-good tidings is Sen. Rudy Boschwitz (R-Minn.). He has warned his fellow Republican, Gov. Al Quie, to "get your political act together"--or withdraw as a candidate for reelection. Quie has been wrestling with an unprecedented $768 million budget deficit.

The senator delivered his message to Quie last month, and in response to a reporter's questions, repeated it in essence today.

The senator's poke created consternation in the ranks of the Minnesota Republican Party leadership, starting with the usually mild governor. Quie chided Boschwitz for "spreading it out in view," and said that Boschwitz has "a lot of Republicans angry with him."

The prod that made the governor so unhappy has an involved history. It originated in a private Boschwitz-Quie conversation in a U.S. Senate corridor a month ago. It surfaced in a copyrighted St. Paul Pioneer Press story Thursday. And apparently the pair also discussed the subject Wednesday night.

Quie was particularly irked that the private conversation came to light just as the legislature failed in its attempt to patch together a bipartisan budgetary solution.

The Pioneer Press reported that Boschwitz was "seriously concerned" about Quie's electability in light of the governor's low standing in public opinion polls. Boschwitz was quoted as expressing fear that "the whole ticket will go down the tube."

Reached today at his Vail, Colo., condominium, Boschwitz praised Quie's competence, integrity and "deep faith," but added, "Any fair-minded observer of political life recognizes that our governor is in trouble. Anyone who sits down and has coffee with friends knows this is true. I've long been one to call a spade a spade. And I privately told the governor I would not sit idly by and see the gains my party made in 1978 jeopardized in 1982."

In the 1978 election--which was dubbed the "Minnesota Massacre" --the Republicans captured the governorship and both Senate seats and made gains in the legislature. Boschwitz is not up for reelection this year, but he said that "at some point" his party's leadership would have to examine all its options objectively because of Quie's political unpopularity.

The benchmark he uses is a Minneapolis Tribune poll that has shown Quie losing sharply. In a poll last October, he ran about 2 to 1 behind former governor Rudy Perpich and Attorney General Warren Spannaus, both key figures in Minnesota's Democratic-Farmer-Labor Party. Spannaus is an announced candidate for governor and has assailed Quie's "fiscal mismanagement," while Perpich, who lost to Quie in 1978, is flirting with a comeback try.

So far, Quie's only overt Republican opposition for the nomination is state Rep. John Ainley, a strong conservative from Park Rapids, who announced earlier that he would oppose Quie because Quie wasn't conservative enough. His quest has not been taken seriously; Quie's approach to economics generally parallels President Reagan's.

Sen. David F. Durenberger (R-Minn.) and Rep. Vin Weber (R-Minn.) were quick to disassociate themselves from the Boschwitz position. Durenberger conceded that Quie has problems but said he felt comfortable being on a ticket headed by him. Durenberger said he was confident Quie would be reelected, although privately he has indicated doubts.

Weber, a first-term congressman from the 6th District, is normally a Boschwitz ally. Thursday, Weber said that the five Minnesota House members had met with Quie about six months ago to question him about his zeal for campaigning--but Weber would not confirm a report that the congressmen shared Boschwitz's doubts about Quie's electability.

Weber said he was "firmly and totally supportive of Al Quie," adding: "Rudy's comments may reflect his personal opinions but he has not spoken for the Minnesota Republican delegation, nor in my judgment, for the Minnesota Republican leadership."