The bridge is meant to facilitate the flow of NAFTA trade into the US, which isn't really good for workers overall, but the construction jobs inherent in the project were enough to win the support of the majority of local trade unions for Snyder's new bridge.
This project is unusual in several ways--in particular, the Governor claims the bridge will be paid for by Canada, and that he does not need legislative approval to borrow the money to pay for it (this whole funding scheme is complicated--I urge you to read up on it if you're interested.) In addition, the project was negotiated by Michigan's Governor and Canadian Prime Minister Harper, without any guidance/framework/approval by the US State Department, Congress, or the President.
A referendum on the bridge issue (which would've required a popular vote to approve the bridge) was one of 6 ballot initiatives that were on the ballot this past November, along with another initiative proposing adding protection for collective bargaining to the state constitution. Governor Snyder, of course, urged his constituents to vote "no" on both measures, despite the support he had received from union leaders in ram-rodding his bridge through.
Given the forgoing, many union leaders must feel betrayed by Snyder, given his RAPID change of heart with regard to support for right-to-work legislation.