U.S. Trade Representative Robert Lighthizer and aides have been consulting with American unions and congressional Democrats over the past few weeks to assemble new proposals aimed at boosting Mexican workers’ rights and wages in talks to overhaul the North American Free Trade Agreement.

The intensifying consultations with labor are part of a gambit to reshape trade politics by winning big Democratic support for the administration’s approach to the Nafta talks, which resumed this week in Mexico City. The Democrats’ votes would...