WASHINGTON — Congressional Democrats, divided and struggling for a path from the electoral wilderness, are constructing an agenda to align with many proposals of President-elect Donald J. Trump that put him at odds with his own party.

On infrastructure spending, child tax credits, paid maternity leave and dismantling trade agreements, Democrats are looking for ways they can work with Mr. Trump and force Republican leaders to choose between their new president and their small-government, free-market principles. Senator Chuck Schumer of New York, elected Wednesday as the new Democratic minority leader, has spoken with Mr. Trump several times, and Democrats in coming weeks plan to announce populist economic and ethics initiatives they think Mr. Trump might like.

Democrats, who lost the White House and made only nominal gains in the House and Senate, face a profound decision after last week’s stunning defeat: Make common cause where they can with Mr. Trump to try to win back the white, working-class voters he took from them, or resist at every turn, trying to rally their disparate coalition in hopes that discontent with an ineffectual new president will benefit them in 2018.

Mr. Trump campaigned on some issues that Democrats have long championed and Republicans resisted: spending more on roads, bridges and rail, punishing American companies that move jobs overseas, ending a lucrative tax break for hedge fund and private equity titans, and making paid maternity leave mandatory.