In the hometown of legendary Notre Dame football halfback George Gipp, the school board decided a few weeks ago to scrap high school athletics for lack of money.

A stone memorial honors Gipp in the northwestern Michigan town of Laurium, where he was a basketball and baseball star at Calumet High School before his early death of pneumonia at Notre Dame in 1920. Twenty years later, Ronald Reagan took his first step toward Hollywood fame with his portrayal of Gipp in "The Knute Rockne Story."

Today, with Reagan in the White House, the Calumet athletic program has become another casualty of the staggering economic dislocation in once-prosperous Michigan. It has suffered more than any other state from the two back-to-back recessions of the last three years. And Michigan's government has suffered along with the workers who have lost their jobs as auto and other factories close down.

State troopers now stop their patrol cars for 15 minutes out of every hour to save on fuel costs. The bureaucracy has been trimmed from 72,300 state workers in August, 1980 to 60,254 last month. Welfare benefits have been cut 11 percent and thousands of recipients taken off the rolls when eligibility was tightened.

When the latest round of cuts is complete, Michigan's budget will have shrunk in one year by an amount roughly proportional to eliminating the entire social security system from the federal budget.

Most states are constitutionally required to balance their budgets each year. In Michigan, the recession has turned this into an endless financial crisis as the state's tax revenues have plummeted and welfare and Medicaid costs have soared.

State budget officials estimate that revenues have fallen 27 percent short of expected spending in the fiscal year that ends this Sept. 30, and in the words of one analyst, "We don't know if we've seen the bottom yet."

To cope, Republican Gov. William G. Milliken, now in his final months in office, has imposed a six-month, 21.7 percent increase in state income taxes, raised state cigarette taxes from 11 to 21 cents a pack, and chopped away at state spending in a manner that far surpasses anything Reagan has been able to win from Congress.

Last week, with only a month remaining in the fiscal year, Milliken asked for another $150 million in state spending cuts, including a $110 million slash in aid to education. This comes on top of $628 million in spending trims from the $4.4 billion budget approved earlier this year.

Michigan's cash crunch has made Wall Street skittish about its borrowings. After the state's credit rating was downgraded, five Japanese banks agreed to back Michigan in borrowing $500 million, ironic and unprecedented foreign aid for the state hardest hit by Japanese economic competition.

The Japanese agreement underscored the fact that Michigan state government remains a pawn in the larger economic chess game, even though efforts are under way to build a more diversified base than just the auto industry. Michigan's budget trauma is severe but not unique. Over the last two years, 40 states have raised taxes and at least half the states have cut spending, according to the National Journal.

With its fortunes inexorably linked to the auto industry, Michigan's economy has always been particularly sensitive to sharp swings in the national economy. After previous slumps, the state bounced back, its treasury flush with revenues generated by a progressive tax system.

This time, the trouble is more fundamental. Hard times have unleashed pent-up demand for services from state government at a time when it cannot deliver as it did in the years when Michigan workers enjoyed some of the highest personal income in the nation.

Gerald H. Miller, Michigan's budget director and Milliken's chief financial adviser, said the state is only beginning to climb out of the economic trough and recovery may take years. "I don't believe we'll ever be back to the peak of 1978-79," he said. As domestic auto makers have lost a large share of the market to the Japanese and high prices discourage sales, Miller said, "I think it has to mean a very slow recovery. You have to say it is going to be a slow transition back."

Such a slow transition means lower expectations in a state that was willing to pay for activist government but now finds it can no longer. "I do believe the quality of life in this state will be reduced because of these budget-cutting efforts," Miller said.

Gerald Vairo agrees. He is a lawyer in George Gipp's hometown who is starting a boosters' club to raise the $40,000 needed to salvage the local high school athletic program. It was eliminated by the school board because of declining state aid, falling enrollments and the defeat of a local initiative -- for the third time -- that would have raised property taxes.

"Michigan is in trouble," Vairo said. "We have reached a point where the financial situation is in a state of ruin. My daughter wanted to take third-year French in school and they cut that out. My other daughter wanted to study advanced biology and that was eliminated. We have roads here that are not fit for man or beast."

The belt-tightening has been widespread, but so far not deep enough to mean the total elimination of any big programs. Instead, everything in sight is being trimmed.

The University of Michigan eliminated its Geography Department. Many local school boards have dropped athletics in the hope that private money would pick up the tab. Michigan state parks remain open, but often there is no one to care for them, except volunteers.

"After all the cuts of the last two years, we are at a very dangerous point," Milliken said in his appeal for the tax increase last spring. "We have cut to the bone and beyond. We have reached a point where further cuts could have a disastrous effect on our future."

Yet last week, Milliken was asking the legislature to approve further cuts.

It has been a painful experience for Milliken, a popular and progressive Republican who, like other GOP governors in the "depression" states of the Midwest, decided to retire this year rather than seek reelection. Even though the economic slump has been largely a national phenomenon beyond his control, Milliken's approval rating among Michigan voters trails that of Ronald Reagan, according to a Detroit News poll published late last month. Said one Milliken aide: "He's not enjoying this one bit."

There is a touch of irony in Milliken's predicament. When he first came into office in 1970, Reagan was ending his first term as California governor, and they seemed to be at opposite poles. Milliken was the compassionate progressive, Reagan the fiscal conservative. Now Milliken is slashing his budget while Reagan rolls up record-breaking deficits.

Milliken doesn't like the role. "I'm not sure I would want to set this up as an example of what is good to do," he said in an interview. "What we are having to do as a result of the recession-depression is take steps that are in my judgment not fundamentally sound."

After the deep 1974-75 recession, Michigan sought to cushion the pain of future slumps. The state established a "rainy day" fund designed "to set aside money in good times to provide a cushion for bad times," said deputy budget director Pat McCarthy. The cushion grew to about $275 million in the growth years of 1977-78, but no one foresaw the depths of what lay ahead. The "rainy day" fund is now dry.

In making their forecasts, state budget officials have repeatedly issued economic projections that proved too optimistic. "We had a lot of company in that," said McCarthy, referring to the Reagan administration's similar difficulties. In Michigan, the result has been year-long budget havoc when revenues dropped more than expected and spending skyrocketed.

In the last two decades, many states have altered their tax systems to parallel the federal government's ability to grow with the economy. The systems became more "elastic," allowing the states to reap the gains of this growth. But when growth slowed, revenues nosedived.

This is what happened with Michigan's "very elastic" personal income tax, said Miller, who estimated that the state would have reaped another $400 million this year alone if auto production had not declined by nearly 50 percent since 1978 levels.

"This is a situation beyond our control," said Milliken.