The group said Snyder reversed his position by not bargaining with the coalition as he did in 2011.
"We were extremely successful bargaining as a coalition in 2011," United Auto Workers Vice President Cindy Estrada said in a statement. "We were able to reach an agreement quickly that was satisfactory for all parties."
The unions said the Snyder administration had offered to either negotiate with the leaders of the five unions as a group without the bargaining committees present, or to negotiate separately with each union.
A spokesman for the Snyder administration said the governor "has always supported the collective bargaining process and he continues to do so."
"We have already been meeting with each union for many weeks and are making good progress on negotiating agreements," said Kurt Weiss, spokesman for the Office of State Employer. "We look forward to continuing that progress and appreciate the good work that's already been done."
But the head of the union for Michigan prison workers said the state was taking a step backward this year.
"Gov. Snyder pledged to continue to work collaboratively with us 2 two years ago," said Mel Grieshaber, executive director for the Michigan Corrections Organization. "Now he's claiming coalition bargaining didn't work. So our question is what has happened in 2013 that has caused him to change his mind?"
Michigan has since become a so-called "right-to-work" state. The law prohibits forcing public and private workers in Michigan to pay union dues or fees as a condition of employment, and applies to labor contracts extended or renewed after March 2013.
The Republican-controlled Michigan Legislature passed the measures last year, and the Republican governor signed them into law.
"Once again, the governor has reversed himself," Michigan State Employees Association President Ken Moore. "He said right-to-work was not on his agenda, that it was divisive, then he rushed to sign it into law amid massive protests. Now he's changed course on bargaining with state employees in a way that's proven successful for workers and taxpayers alike."
Weiss said the joint bargaining was unwieldy.
"When it comes to coordinating bargaining with more than one union, we believe the process can be made more efficient and effective by meeting collectively with leaders and a smaller number of representatives as we did when the final agreement was reached in 2011 rather than with nearly 100 people in a bargaining room."