The National Treasury Employees Union and the National Federation of Federal Employees, with a combined 260,000 members, issued the call for a "federal employee call-in day" Monday.
The current continuing resolution funding the government expires at midnight Friday.
"I believe that a two-minute phone call from a constituent who is a federal employee, explaining to an elected official why it is vital not only to continue government operations but to fund them adequately for the good of the country can change the debate on this issue," said NTEU President Colleen Kelley.
She also denounced House Republicans' "extreme" budget cuts.
"Furloughing hundreds of thousands of federal workers would be devastating to local economies," said NFFE President William Dougan. "With 85 percent of the federal workforce living outside of Washington, D.C., communities across America would feel the pinch."
Employees will be urged to have their family and friends make calls as well.