Some Detroit union leaders accuse Mayor Dave Bing and the city of backing them into a corner by refusing to negotiate new collective bargaining deals with less than a month before some of the contracts expire.
Union strategy sessions continue to focus on what could be a June 30 contract showdown.
ASFSME Council 25 spokesman Ed McNeil says workers know they "can't trust" the city "at this point."
Detroit Police Officers Association president Joseph Duncan says there has been no bargaining since unions agreed earlier this spring to concessions to help stave off a state-appointed emergency manager.
Part of a consent agreement with the state calls for the city to have negotiated or imposed new labor deals by July 16.
Detroit faces a budget deficit of more than $200 million.