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The truck drivers are targeting four companies for now, but may expand the strike, according to Teamsters spokeswoman Barb Maynard.
Nebraska Sen. Deb Fischer says labor impasse sent "ripples through the U.S. economy."
Schnitzer Steel and Bed Bath & Beyond say the labor slowdown and resulting port congestion hurt business.
House and Senate committees voted last week to extend the expiring trade preference programs.
Coast Guard organizations of Italy and Malta, along with merchant vessels, are bearing the brunt of rescue operations for migrants at sea.
Hutchison Port Holdings plans to invest $303 million by 2019 to expand the Oman International Container Terminal at the Port of Sohar, quadrupling container handling capacity at the port.