The Senate included a full-year appropriations bill for the Department of Homeland Security (DHS) in the continuing spending bill, and the House quickly approved it last week. Barber said that bill must be used to restore funding to agents working the U.S.-Mexico border.

"Security of the U.S.-Mexico border is paramount and requires the full-time presence of our Border Patrol agents," he wrote. "Funds for staffing and necessary overtime must be given top priority."

Barber also urged Napolitano to find cuts elsewhere in her department in order to make whole the budget for U.S. border agents, and present a "clear plan" to the public showing how DHS will continue to protect the border.

"Every department expense must be scrutinized because lower-priority expenditures come at the direct sacrifice of our agents, their families and the safety of my constituents," he wrote.

"I also ask that you present Congress and the American people a clear plan that assures that our borders will be protected and our border patrol agents respected for the work they do."

Like other agencies dealing with the sequester, DHS warned many federal workers under its purview that they would be subject to furloughs. Barber said DHS told border agents in the Tucson sector of the southern border that they would be furloughed and see salary cuts up to 40 percent.

He said would hurt the families of these workers, lower their morale, and also contribute to a more dangerous border.

"My district still is the most porous sector of the border with Mexico," he wrote. "The reduction of border patrol agent hours will invite even more smuggling through the region and will increase the dangers to the people I represent."