Detroit’s budget impasse continued into this week after Mayor Dave Bing’s weekend meetings with City Council members failed to yield a breakthrough.

Bing and the council have been locked in debate for weeks over the size of cuts and the city’s deficit.

Members in a special session last week voted 7 to 2 to override Bing’s veto of the council’s budget, which cut $31 million from his $3.1 billion spending plan. They said they imposed the additional cuts after the council’s fiscal analyst warned that the mayor’s revenue projections were too optimistic.

In response, Bing’s office released a report detailing the effect that the cuts would have on city services, and warned they would mean more layoffs.

The fiscal 2011 budget is the first for Bing and most of the City Council. Most incumbent members were defeated in last year’s election.

“We were elected — or re-elected — on a platform of change, and openly committed to communicating and working together in the best interest of the citizens,” Bing said in a statement Friday. “Council’s decision to ignore a six-month process of careful operational and financial analysis after only a six-week review is nothing less than irresponsible.”

In an op-ed piece in last Sunday’s Detroit Free Press, City Council President Charles Pugh wrote that the council’s budget will allow Detroit to avoid ­bankruptcy.

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