CUTLER BAY, Fla. -

More Miami-Dade Fire Rescue engines sat idle Tuesday as the department maintained its "rolling brownouts" after exceeding its overtime budget.

A fire engine in Cutler Bay and an ambulance in North Miami were two of seven units offline.

"Time is brain and time is heart," said Miami-Dade Fire Rescue Lt. Richard Ramirez. "That's all going to exacerbate the situation that you have medically."

Protesting firefighters warned of possible delays in response times as the department is contractually unable to pay overtime because it exceeded its overtime budget.

"It's a giant, complex puzzle that our operations chief has to do," said Miami-Dade Fire Rescue Div. Chief Louie Fernandez.

"We never intended for them to not hire firefighters," said Miami-Dade firefighter Will Fleitas. "In the last five years, we have hired no new firefighters or paramedics.

Countywide, calls for service increased from 235,629 in 2011 to 238,800 in 2012, according to the department, which has 92 fewer responders since 2010.

"The fact that we're continuing to be lacking bodies and the call volume is still there, you're going to get to the point of -- not only putting the residents in danger -- but [also] us doing our job," said Fleitas.

The rolling brownouts will continue until the new fiscal year.