Amid a payroll scandal that keeps unfolding, Gov. Charlie Baker's Democratic challenger Jay Gonzalez is calling for the removal of Baker's public safety chief and the State Police colonel, but top Democrats are siding with Baker's wait-and-see approach.

"In short, I think the call by Mr. Gonzalez is at best premature," Rep. Harold Naughton, the House chairman of the Legislature's Public Safety and Homeland Security Committee, told WGBH News.

"I think they've taken decisive action, and I think they've taken appropriate action. And I think that's indicated by the indictments that came out this week and other moves that they've [made] to enhance internal affairs and auditing within the force," Naughton said, adding that the Special Commission of Lawmakers formed to look into possible reforms to the State Police held its first meeting Wednesday.

Gonzalez says Baker was too slow to investigate the State Police after reports surfaced that troopers were abusing the payroll system, and he wants Colonel Kerry Gilpin and Public Safety Secretary Daniel Bennett gone.

"Every day it feels like there's one new revelation after another," Gonzalez said outside the State House Wednesday morning. "The reports about the fact that the Baker administration, Colonel Gilpin and Secretary Bennett have been draggin' their feet doing anything about it is really frustrating."

Gonzalez says Baker should fire Gilpin because she signed off on earlier investigations that cleared some troopers who were later charged, as well as Bennett, the head of the executive officer that oversees the State Police.

House Speaker Robert DeLeo admits that the issues facing the State Police are "serious and troubling," but didn't join the call for Gilpin and Bennett's removal. DeLeo expressed faith that legislative reforms made to the way troopers operate and ongoing investigations will bear results.

"We expect the new hiring and management oversights in place will allow for the must needed changes to regain the public trust," DeLeo said in a statement.

Senate President Karen Spilka did not respond to requests for comment on Gonzalez's position.

Baker is standing by his appointees. The governor says the investigation launched when Gilpin took over last November has lead to the eight trooper indictments so far.

"She's the one that lead the investigation, expanded it, and she's the one that submitted the documentation to the attorney general and U.S. attorney's office," Baker told reporters Wednesday afternoon.

Dozens of additional troopers still under investigation by state and federal investigators.