Mr. Trump’s divisive and at times demagogic presidency has ignited much of the liberal upheaval, driving many left-of-center voters on to a kind of ideological war footing. That has translated into a surge in outsider candidates in the midterms who are pressuring Democratic leaders to support an ambitious liberal platform that includes single-payer health care, free college tuition and the abolition of the Immigration and Customs Enforcement agency.

But this insurgency, which is both encouraging and alarming Democratic officials, is not merely aimed at pushing the party farther left ideologically. There is a deeper divide over how far to go in confronting Mr. Trump and attempting to thwart his agenda.

At a strategy session held over lunch last week, Senate Democrats settled on a careful strategy for the coming Supreme Court confirmation battle. They would drop their demands that Republicans not appoint a replacement for Mr. Kennedy until after the midterm elections, senators decided, and instead would highlight the threat to abortion rights and health care to try to mobilize opposition to Mr. Trump’s appointment.