The United States is making headway on two historic trade agreements, one with 11 countries on the Pacific Rim and another with America’s friends in Europe. These two agreements alone would mean greater access to a billion customers for American manufacturers, farmers and ranchers.

But before the U.S. can complete the agreements, Congress needs to strengthen the country’s bargaining position by establishing trade-promotion authority, also known as TPA, which is an arrangement between Congress and the president for negotiating...