Border Patrol agents had been bracing for a big hit on their pocketbooks.

For weeks, they have labored under a threat of unpaid furlough days and the elimination of overtime, a powerful combination that placed them among the federal employees who had the most to lose from the budget cuts known as sequestration.

On Monday, Customs and Border Protection (CBP) postponed that threat. There’s a sigh of relief coming from Border Patrol agents, but no cheers.

“For now, people can breathe easy . . . but we don’t know for how long,” said Thane Gallagher, a Border Patrol agent based in San Diego, speaking as a union member. “It’s good news for now.”

There has been other good news, of a limited sort, on the furlough front. It’s all in the context, however, of continued serious budget cuts. The CBP decision follows Thursday’s Defense Department announcement that its employees would have 14 furlough days that would begin in June, instead of 22 as originally planned. That same day, Attorney General Eric H. Holder Jr. told staffers he is “postponing until mid-April any decision about the need to institute furloughs for DOJ employees.”

“The situation with the budget has been very fluid,” Holder said in his staff memo, which was obtained by The Washington Post.

Days earlier, Justice had announced it was canceling furloughs for federal prison staffers.

CBP, like Defense and Justice, changed course after President Obama signed an appropriations law last week that allows limited flexibility in implementing the spending cuts.

“In light of the Fiscal Year 2013 Appropriations bill and sequestration impacts, U.S. Customs and Border Protection is re-evaluating previously planned furloughs and de-authorization of Administratively Uncontrollable Overtime (AUO) and will postpone implementation of both at this time,” CBP said in a statement. “Although the budget reductions imposed by sequestration are significant, the bill’s provisions allow CBP to mitigate to some degree the impacts of the reduced budget on operations and on CBP’s workforce. CBP continues to assess the exact impact the legislation will have on our operations and our workforce.”

A memo from Thomas S. Winkowski, CBP’s deputy commissioner, to employees said much the same thing. Their reaction was muted.

Shawn Moran, vice president of the National Border Patrol Council, which is affiliated with the American Federation of Government Employees, said the union “is cautiously optimistic about CBP’s decision to postpone furloughs and the de-authorization of AUO. We do have a well-founded fear that CBP will not do the right thing, though, and ultimately make a decision that will leave the border in an insecure state.”

While pleased with this action, union Local 1613 cautioned its members to take nothing for granted.

“This is not over,” says a notice on the Local’s Web site. “We are like death row inmates who got a temporary stay of execution. It is a delay not a guarantee! We need to keep up the fight and keep the public and media involved and interested.”

Execution is pretty close to the way Gallagher felt the cuts would have hit him.

Even with just the elimination of overtime, the financial “burden will be catastrophic,” he said before Monday’s CBP postponement was announced. Like other Border Patrol agents, Gallagher regularly works at least 50 hours a week and depends on the overtime, a consistent part of his pay.

“It’s freaking me out. I’m still expected to take a bullet for a hell of a lot less money, and I can’t stomach that,” he said.

He’s still expected to take a bullet, but at least his pay isn’t being cut — at this time. Agents believe that stories about the cuts in border protection, in agents’ pay and congressional pressure all pushed the agency to rethink its plans.

Last month, four House members from Texas sent a letter to Speaker John A. Boehner (R-Ohio) and Majority Leader Eric Cantor (R-Va.) protesting planned CBP spending cuts.

“Texas is among the states that will feel the sharpest sting from cuts to CBP,” the letter said.

The combination of unpaid furlough days and the elimination of overtime would result in agents losing up to 40 percent of their pay, according to the letter from Democratic Reps. Henry Cuellar, Beto O’Rourke, Ruben Hinojosa and Filemon Vela. That would have amounted to $6.18 million every two weeks for agents in Texas, the lawmakers estimated.

Furthermore, “the operational impact to border security is unthinkable,” they said. “The loss of AUO and the furlough will equate to fewer agents in the field and . . . will also impact their ability to effectively patrol and respond to calls to ranches along the border.”

Springing news about postponing furloughs and overtime cuts on this particular Monday left some agents wondering.

“A lot of agents are still kind of skeptical on the whole thing, being that it happened on April 1st, April Fools’ Day,” said an El Paso officer who spoke on the condition of anonymity in order to discuss agency-related business.

“This whole thing could happen again in another month or two.”

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