The strained immigration talks between the U.S. Chamber of Commerce and the AFL-CIO are being tested further by a demand from unions that represent construction workers.

The influential business lobby and labor federation have been negotiating for weeks in hopes of reaching an agreement on how best to overhaul the nation’s immigration system. Consensus between the two sides could inject momentum into the legislative efforts that are under way Congress.

But the talks hit a rough patch last week when the Chamber and the AFL-CIO sniped publicly over how many visas should be available in a program for temporary workers.

Unions for construction workers are griping about the number of visas asked for by the Chamber and are demanding that their industry be exempt from the temporary worker program altogether.

“In the construction industry, there is no need for temporary workers. Period,” said David Mallino, legislative director for the Laborers’ International Union of North America (LIUNA).