We Are Ohio said Friday that the time for a compromise had passed.
Public employees said they wanted to talk months ago, and think Kasich's invitation is more political than polite.
"Let me just say, the timing is pretty suspect," Dayton Fraternal Order of Police President Lt. Randy Beane said. "You know, we're getting ready to go into national elections and certainly all eyes are on Ohio, and what's going to happen here."
Kasich denied that allegation.
"I don't think when they approached us they thought they were going to lose. We don't think we're going to lose."
The law signed in March bans public employee strikes for more than 350,000 workers. It also allows public worker unions to negotiate wages, but not health care, sick time or pension benefits.