Rev. Jesse Jackson has said he wants to work with transit officials and the unions to see if they can work out a deal to put employees back to work.
The CTA is working to close a $95 million budget shortfall.
Saturday, Jackson said his goal was two-fold: getting workers back to work and providing service to the people who need it most.
However, he acknowledged there are profound challenges.
"Where's the money going to come from? The state's facing a deficit. Where's the money going to come from? So is the city. Where's the money going to come from? It can't all come out of the workers hide," Jackson said.
Jackson also questioned plans for high speed rail service from Chicago to St. Louis, saying officials need to extend train service in Chicago first.
Union officials said Saturday they had given two money-saving proposals to CTA officials last week but were waiting for a response.