The ongoing stalemate over U.S. immigration policy is getting costly.

Congressional Republicans continued on Tuesday to debate a potential funding cut for the Homeland Security Department to block President Barack Obama’s executive order deferring the deportation of millions of unauthorized immigrants.

If they follow through with the threat, the shutdown could sideline some 30,000 administrators and other workers. Most workers would be exempt, as another 200,000 fall into essential categories such as Border Patrol, Secret Service and Transportation Security Administration. Those workers would remain on the job but without pay until the funding standoff is resolved.

Obama warned Monday that the payroll suspension would be felt hardest in regions covered by border patrol, port inspection and airport security agents.

“It will have a direct impact on your economy, and it will have a direct impact on America’s national security because their hard work helps to keep us safe,” Obama said.

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The president’s order to defer deportations was put on hold last week by a federal judge, who sided with officials from Texas and 25 other states that took the White House to court. The administration is appealing the ruling but has suspended plans to allow undocumented immigrants to apply for legal status.

The loud, ongoing legal and political debate unfolding over immigration reform often overlooks one very important impact from letting more foreigners come to live and work in the U.S.

Read MoreImmigration stalemate: The economic toll

Many researchers believe it’s good for the economy.

The economic case for a major immigration overhaul is that with an expanded workforce, the economy will grow more rapidly and the government will collect more in taxes, lowering the federal deficit.

And because immigrants tend to be younger, on average, than the general U.S. population, the influx of new workers would help offset the economic burden of the rising cost of caring for an aging population.