The USDA has said that U.S. meat processors, who would have to essentially shut down while inspectors were laid off, would lose about $10 billion in production.

Vilsack said in a February 12 letter that, although furloughs are "the least desirable option," there was no other way to satisfy the impending cuts.

The USDA will close 259 domestic offices, facilities and labs across the country, as well as seven foreign offices.