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Rickmers, which manages the ship for Maersk said Iranian navy fired "warning shots" at Marshall Islands-flagged Maersk Tigris.
A strike could come as soon as Monday, according to a statement from Teamster affiliate Justice for Port Truck Drivers.
The International Longshore and Warehouse Union said 82 percent of its members voted in favor of ratification.
Trade Promotion Authority gives the White House more freedom to negotiate major free trade agreements with Pacific Rim and European partners.
Cuba has pent up demand for trade and U.S. companies are eager to tap a new export market.
The Senate approved another short-term extension to continue funding highway, bridge and transit projects.