WASHINGTON — Two days after midterm congressional elections that handed them control of the House, triumphant Democrats dialed in to their first conference call since winning the majority to strategize on the way forward.

But the call that Representative Nancy Pelosi of California, the minority leader, convened on Thursday with Democratic lawmakers and their newly elected colleagues was not a planning session on how to protect health care coverage or lower prescription drug prices, thematic pillars of the party’s successful campaigns. It was a briefing about President Trump’s latest remarkable move — his decision, hours after the last polls closed, to fire the attorney general — and a discussion of how Democrats would address the cascade of potentially grave constitutional consequences that could follow.

The strategy session highlighted the central challenge that Democrats face as they prepare to assume control of the House in a new era of divided government that begins in January. Democrats, who remained remarkably focused during their campaigns, must now figure out how to put forward their own agenda — one Ms. Pelosi says will be focused on lowering drug costs, rebuilding the nation’s roads and bridges, and cleaning up government corruption — even as they deal with the provocations of a president who relishes confrontation and disdains institutional norms.

“Trump’s great genius is to try and reduce everyone to his level and approach, and he wants to be able to paint Democrats as single-mindedly bent on his destruction,” said David Axelrod, a Democratic strategist and former top adviser to Barack Obama. “These Democrats didn’t get elected, by and large, to war with Trump. They got elected to try and get some positive things done on issues like health care and economic issues for their constituents, and the notion that on Day 1 they should spend all their energy trying to bedevil him is wrong. Striking the balance is going to be difficult.”