Gerard Fitzgerald is the president of the UFA, the Fire Department of New York's largest union, and he said that while he knows funding is the issue, the FDNY shouldn't be threatened.
"But to put it on our backs, to threaten us to go to Washington to try and get more money, it's just unacceptable," Fitzgerald said at a Wednesday evening news conference.
Wednesday morning on CNN's New Day, de Blasio told John Berman that New York City's economy has already lost $7.4 billion and without a fourth federal stimulus, he's looking at furloughs and layoffs of first responders.
De Blasio said "the heroes in this crisis" -- first responders, healthcare workers and educators -- are facing furloughs in cities and states all over the US because of the economic strain of the pandemic at a time when they should be celebrated.
"How will we support these people who we need if we don't have any money?" he said.
CNN reached out to de Blasio's office Wednesday evening for reaction to Fitzgerald's remarks, but has not received a response.
FDNY members work long hours and risk exposure Fitzgerald said that FDNY members are working long hours, watching others fight for their lives during the pandemic, all while worrying they brought the virus home to infect their families.
"And less than one month after we were receiving record high call volumes, the likes of which we haven't seen since September 11, our mayor, who's chief duty is to protect the people of the city, suggests that our jobs are dispensable," Fitzgerald added.
"And the very people whose heroism is on display every single day during this pandemic are the ones who will suffer because of it." Fitzgerald added: "I'm furious over this and I believe that anybody that's in the city of New York should want and expect the greatest services in the world -- and we are that service," he said. "And to threaten our jobs is just unacceptable."
De Blasio and Fitzgerald agree federal funding is critical The work cities and states have done to battle the virus has been done largely without the help of the federal government, de Blasio said, citing testing as an example.
But he said state and city governments will need the help of the federal government to recover.
"The only place that prints money, the only place that can provide the help to get us out of this mess is the federal government," he said.
Fitzgerald said Washington needs to overcome politics and band together to get the funding to cities and states that need it.
"There's lives at stake whether you're a red state or blue state. They need to get together and stop messing around with people's lives," Fitzgerald said. "Give each city or each state, the money, the funds, the people that they need to combat this virus to keep their citizens safe."
"Band together and let's get some things done that are a necessity for cities like New York and other cities across the country that are battling this pandemic in this way."
CNN's Madeline Holcombe contributed to this report.