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The city has operated since last spring under a previous consent agreement with the state that allows state review over Detroit Mayor Dave Bing’s efforts to restructure city finances. If he hits established benchmarks, the state releases bond money that it has held in escrow.

That consent agreement averted earlier calls for an emergency-manager takeover, but as time has passed with no broader solutions on the horizon, the governor, who has remained patient with the city, may have to step in.

“The governor, he probably doesn’t want to do it, but there is nothing the local leadership has shown that they are willing to put this type of plan on the table and are willing to be aggressive about it,” said Mr. Foster, whose consulting firm has approached the city with its own blueprint for fiscal change, which he said has been tepidly received.

Michigan voters in November repealed an existing financial-manager law for the state. It had been used successfully in several cities, including Flint and Benton Harbor and in school districts including Highland Park and Detroit Public Schools but had drawn criticism that it took management of a municipality away from the people who had been elected to do so.

Just five weeks later, however, the state’s Republican-led Legislature passed a newly drafted version of the emergency-financial-manager statute, restoring state power to take over cities that cannot manage their finances. It takes effect in late March or early April.

How an emergency manager’s takeover for Detroit, the state’s largest city, plays out politically is unclear. Mr. Bing has jousted repeatedly with his city council over reform measures but made little headway. The entrepreneur and former NBA star has not yet said if he will seek re-election next year. He took over for disgraced mayor Kwame Kilpatrick in 2009 and was elected that year to serve a full term.