WASHINGTON — Two of the Democratic Party’s most loyal constituencies, labor and environmentalists, are clashing over an effort to raise tens of millions of dollars for an ambitious voter turnout operation aimed at defeating Donald J. Trump in the November election.

The rift developed after some in the labor movement, whose cash flow has dwindled and whose political clout has been increasingly imperiled, announced a partnership last week with a wealthy environmentalist, Tom Steyer, to help bankroll a new fund dedicated to electing Democrats.

That joint initiative enraged members of the nation’s biggest construction unions, already on edge about the rising influence of climate-change activists. The building-trades unions view Mr. Steyer’s environmental agenda as a threat to the jobs that can be created through infrastructure projects like new gas pipelines.

The dispute, laid bare in a pair of blistering letters sent on Monday to Richard L. Trumka, president of the A.F.L.-C.I.O., underscored the tensions between the two pillars of the Democratic coalition.