CHICAGO — In the search for models to navigate the nation’s unemployment misery and the states’ budget woes, Michigan is rarely mentioned.

After all, years before the rest of the country fell into recession, Michigan, so vested in the automobile industry, was wrestling with a single state downturn — and one that just kept going until the rest of the country unhappily caught up. And years before the rest of the states found themselves trying to patch state budget holes because of falling tax revenues, Michigan was staring at gaps to fill.

And yet, Jennifer M. Granholm, the former Democratic governor of the state, who led it through much of its rocky last decade, says she sees a key lesson from Michigan — a warning, perhaps, more than a model — for the rest of the nation as it tries to create jobs and emerge from an economic funk.

“Everything that is hitting the country hit Michigan first,” Ms. Granholm said in an interview, reflecting on eight years in office in which the state’s economic crisis overshadowed all else. Her response to the crisis, she said, was to cut spending, cut government jobs, cut taxes — the very approach now being promoted elsewhere, particularly after Republican victories in statehouses around the country in 2010.