(CNN) Comedian Jon Stewart joined advocates on Capitol Hill on Monday to pressure White House budget director Mick Mulvaney to abandon a proposal that they say could threaten health care treatment for 9/11 first responders.

During Monday's meet-up, the former Comedy Central "Daily Show" host chided Mulvaney for trying to separate the World Trade Center Health Program from the National Institute of Occupational Safety and Health.

"It is a special kind of incompetence that takes a program that was fought for for 15 years by firefighters, police officers, first responders, veterans and survivors, that has finally come to fruition, and is finally working well -- it is a special kind of incompetence to want to turn that upside down," Stewart said.

The White House did not immediately respond to a CNN request for comment.

The World Trade Center Health Program -- which is currently housed under the National Institute of Occupational Safety and Health -- provides monitoring and treatment to more than 80,000 people who suffer from illnesses while working at Ground Zero, and advocates fear that the change would harm the program.

Read More