CHICAGO — After weeks of escalating debate with Mayor Dave Bing, the Detroit City Council Thursday approved a compromise $3 billion 2012 budget that restores half of the $50 million the council had trimmed from Bing’s original proposal.

Restoring the cuts means the mayor avoids what he warned would be large layoffs and service cuts starting Friday.

The budget debate was colored by warnings from both Bing and council critics that the city faced a takeover by the state if officials failed to adopt a balanced spending plan.

With a new budget in hand, Bing said Detroit’s next challenge is winning Michigan’s approval of a five-year deficit elimination plan that restores the city to stability — with a small surplus — by 2016.

The city has a $155 million structural deficit that could balloon to $1.2 billion by 2015 without action, according to the mayor.

The final all-funds spending plan totals $3 billion, slightly larger than last year’s due to a planned $300 million water revenue bond sale.

The water bond sale, as well as Detroit’s planned issue of $125 million of bonds to finance a new light-rail project on its main thoroughfare, both require state approval.

The general fund budget totals roughly $1 billion. Bing’s plan relies on several revenue-generating proposals that still require the approval of the Michigan Legislature.

City Council members were skeptical of the mayor’s revenue estimates and the assumption of legislative approval. The council trimmed $50 million from his proposed budget to replace what they deemed were “soft revenues.”

The administration later said it had found additional revenue and pushed an amendment that would have restored $30 million of the cuts.

The council rejected the amendment Tuesday, prompting Bing to declare he was done negotiating and was now preparing for major layoffs. But the next morning he came back to the table with a $25 million amendment compromise. The council approved that amendment Thursday morning.

Bing was greeted by loud applause when he entered council chambers after they approved the budget. “I have nothing to say but thank you very much and it’s time to go to work,” he told the council.

“It’s been a tough process, but at the end of the day we worked out a deal that works for everyone,” the mayor said later. “Eliminating our deficit is the next challenge for us.”

The final amendment taps $20 million in funds from an escrow account set up for the city’s incinerator that will be released three years early and $5 million from various sources. It does not include $10 million of state revenue aid that the administration wanted to include.

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