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The U.S. Customs and Border Protection agency said Monday it will delay furloughs and the elimination of planned overtime, after announcing last week it would implement such cuts to deal with sequester -- the roughly $85.4 billion in mandatory federal budget reductions this year across all government agencies.

The border agency said the cuts will be delayed “pending re-examination,” following concerns from Congress and at least one border agent union about potential safety and security lapses.

Deputy Commissioner Thomas S. Winkowski told employees in a letter Monday that the temporary spending bill President Obama signed last week that funds the federal government over the next six months allows the agency to “mitigate to some degree” the sequester's impact.

However, sources told Fox News a recent surge in illegal border crossings contributed to the re-examination, as the Senate nears a final proposal on immigration reform that hinges on secure borders.

Still, the agency must find ways to cover a $250 million shortfall this year as a result of the sequester.

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Congress agreed in 2011 on the mandatory, across-the-board cuts this year as leverage to get the two sides to agree on a less drastic approach to reducing the federal budget. But the two sides failed to reach a follow-up agreement before the March 1 deadline. The cuts equal roughly $1.2 trillion over the next 10 years should Congress allow them to continue.

The agency also Monday pushed back on reports that border agents have seen the number of illegal crossings double recently, amid the looming cuts.

Bill Brooks, an agency spokesman, said border patrol apprehensions remained at historic lows in fiscal 2012, with fewer in Arizona, California and New Mexico, “reflecting” less people crossing the border.

He also said the Department of Homeland Security, under the Obama administration, has “dedicated historic levels of personnel, technology and resources" to the country’s Southwest border with Mexico.

However, Brooks acknowledged an increase in apprehensions in south Texas.

The immigration reform proposal being crafted by a bipartisan group of eight senators is expected to include provisions that U.S. borders be secured before allowing a path to citizenship for at least some of the estimated 11 million illegal immigrants now in the country.