WASHINGTON — When House Democratic leaders hastily called a news conference Wednesday to demonstrate their outrage at President Trump’s latest dramatics, they took great pains to show they were not seeking to railroad him out of the White House.

“No one ought to, in my view, rush to embrace the most extraordinary remedy that involves the removal of the president from office,” said Representative Adam B. Schiff of California, the sober-minded senior Democrat on the House Intelligence Committee. He warned that Democrats should not let their actions “be perceived as an effort to nullify the election by other means.”

At that very moment, Representative Al Green, Democrat of Texas, was in the well of the House thundering, “The president must be impeached!”

The barrage of reports about Mr. Trump’s chaotic and controversial administration has helped revive Democrats, raising their hopes that they can ride a Trumpian backlash to great success in next year’s elections. But with the cloud over the White House darkening each day, liberal activists are courting a backlash of their own as they demand of their lawmakers nothing short of driving the president from office by any means necessary.