With Republicans likely to retain control of the Senate, the odds of even a vaguely progressive bill of any real significance making it through the upper chamber are slim. It’s hard to imagine Mitch McConnell, the Senate Republican leader, allowing his members to come within 100 miles of, say, a costly infrastructure plan. But this, too, could work to the Democrats’ advantage.

By pushing issues that the president specifically and aggressively promoted on the campaign trail this year, House Democrats could turn up the political heat on Senate Republicans to take awkward votes on popular issues. If Mr. McConnell declined to take action, as is so often his way, Democrats could hammer home the contrast between their let’s-get-stuff-done attitude and Republicans’ obstructionism. Along the way, they might even find a way to drive a wedge between Republican lawmakers and the president.

As for Mr. Trump’s incentive to reach across the aisle: The man likes to win. It may well be the only thing he cares about. Republican lawmakers acknowledge that he often doesn’t give a flip about the specific contents of a deal, so long as he can climb aboard and declare victory.