A billionaire keeps pushing to impeach Trump. Democrats are rattled.

Democratic leaders have pressed Tom Steyer privately, urging him to tone down his campaign calling for President Trump’s impeachment. They have prodded him in public, declaring on television that they consider impeachment an impractical idea. And party strategists have pleaded with Democratic candidates for Congress not to join in.

But Mr. Steyer, a California billionaire and one of the Democratic Party’s most prolific donors, has only intensified his attacks in recent weeks. Buoyed by tens of millions of dollars in television commercials — financed out of his own pocket and starring him — Mr. Steyer has become one of Mr. Trump’s most visible antagonists, firing up angry Democrats and unnerving his own party with the ferocity of his efforts.

Mr. Steyer is likely to unsettle national Democrats further in the coming weeks, with a new phase of his campaign aimed at pushing lawmakers in solidly liberal seats to endorse impeachment. Having collected more than four million email addresses from people who signed an impeachment petition, Mr. Steyer has begun prodding those voters to call congressional offices and lobby them for support.