Hundreds of MBTA workers wearing orange T-shirts and waving signs critical of Gov. Charlie Baker's move to privatize certain public transit operations rallied on the steps of the State House Thursday afternoon in an escalation of what has become a deepening point of contention between the governor and Democrats.Boston Mayor Marty Walsh, who has enjoyed a cozy relationship with the Republican governor over the past two years, lent his voice to the cause as more than two dozen Democratic legislators and members of the Boston City Council showed up in solidarity with T workers."There has to be cost savings here somewhere, but you're not going to make up a hundreds of millions of dollars deficit by wages only. You have to do it by other reforms inside the organization," Walsh told reporters before addressing the workers.Walsh, a former union official and state representative, said the MBTA has been dealing with a structural budget deficit since before he first came to public office in 1997, predating Baker and his predecessor Gov. Deval Patrick.The mayor said he was worried that the moves to privatize money-counting operations at the T and to explore the outsourcing of other operations such as fare gate maintenance could become a slippery slope. He also questioned whether the contracts being signed were producing the savings promised."I will stand with you until this issue is over," Walsh told a cheering crowd, which broke into a "Marty for Governor" chant.As the protest continued beneath his third floor office on Thursday afternoon, Baker held a quiet ceremony with a handful of firefighters and lawmakers to sign into a law a bill intended to improve fire safety.Addressing the protest outside and Walsh's call for Baker and the head of the T to sit down with union leaders to find a path forward for the T that doesn't involve privatizing jobs, the governor said he has met with union officials several times and continues to be engaged in discussion."I've said many times it's important for us to ensure that the T is a highly functioning and effective, reliable and dependable transportation system for the millions of Massachusetts residents who ride it and for all of the taxpayers and riders who pay for it.The T is currently in discussions with the union and we are all hopeful that those will lead to positive results," Baker said.Earlier in the day in a WGBH radio interview, Baker defended the decision to outsource "money room" operations to Brinks."The money room has been a perennial source of operational, financial and public embarrassment to the MBTA for years and years and year and years and years. I'm old enough to remember the stories in the 90s and the 80s associated with the money room.It's not the core mission of the MBTA," Baker said on "Boston Public Radio" in response to a caller.The governor said MBTA workers in the money room have "never been able to reconcile" the cash collected from riders, while other public transit systems around the country can account for collections "to the penny.""The T should do the things that the T is good at and that has to do with moving people around, a million people a day across the transit system and it should find others who are good at doing things like this, like Brinks, and have them do it," Baker said.The governor noted that money room workers have not lost their jobs, but will be working in other departments at the MBTA. Through reforms like the private contract with Brinks, Baker said the T has saved $70 million in its operations budget while putting more people to work driving buses.T workers, however, made clear that they fear for their jobs. Displaying signs on poles and taped to the Robert Gould Shaw Memorial on Beacon Street reading "Keep Public Transportation Public," workers cheered speakers who praised the day-to-day work to move Bostonians around the city."The MBTA has to stop this privatization train," said James O'Brien, president of the Boston Carmen's Union, accusing the MBTA administration of exaggerating the potential for savings from privatizing the money room.O'Brien knocked Keolis, the private French operator of the commuter rail who has been fined repeatedly for poor on-time performance and other issues, as evidence of what can happen when transportation is put in the hands of a private operator.Walsh said he has had "decent conversations" with the Baker administration about their plans for the T and hopes the dialogue will continue."There's a structural problem here and you can't balance it on the backs of workers," Walsh said.Democratic lawmakers in 2015 gave Baker the authority to more easily pursue the privatization of MBTA services as part of an MBTA reform package written into the state budget.Among the politicans who attended the rally were Sens. Linda Dorcena Forry, Thomas McGee, Dan Wolf, Michael Rush, Jamie Eldridge and Joe Boncore and Reps. Dan Cullinane, Michelle DuBois, Nick Collins, Jay Livingstone, Claire Cronin, Bruce Ayers, Dan Hunt, Ed Coppinger and Boston City Councilors Michelle Wu and Andrea Campbell.