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. In an interview, Mr. Steyer was dismissive of party leaders’ reservations about making impeachment an issue in 2018. He described Mr. Trump as lawless and unfit for office; acknowledging the practical obstacles to impeachment, he said raising a popular outcry was a necessary first step. “We’re just telling the truth to the American people, and it’s an important truth,” Mr. Steyer said of his campaign. “And if you don’t think it’s politically convenient for you, that’s too bad.” Already, Democrats acknowledge that Mr. Steyer has helped force impeachment into mainstream conversation, playing to a liberal base that has cheered confrontational tactics like the three-day government shutdown. While Democrats intend to run on a fiercely anti-Trump message this year, party leaders envision a campaign of broad attacks on the president’s economic agenda rather than a blunt-force impeachment pledge. There is no realistic chance of impeaching Mr. Trump while Republicans control Congress, and Democrats from moderate and conservative districts fear the idea could alienate voters otherwise likely to vote their way in November. But the Democratic base, enraged by Mr. Trump and frustrated by party leaders counseling restraint, appears enthusiastically open to seeking the president’s removal. A handful of Democratic congressional candidates — in crucial states like California, Florida, Nevada and Wisconsin — have vowed to pursue impeachment if they are elected. That number is likely to grow during the coming season of Democratic primaries, in which throngs of candidates are competing for the affection of liberal voters who loathe the president. Mary Barzee Flores, a former circuit court judge who is one of more than a half-dozen Democrats seeking a Republican-held seat in Miami, said the issue had plainly resonated with voters in the area, where Mr. Trump is unpopular. Ms. Barzee Flores, who endorsed impeachment in a newspaper column last fall, said Mr. Trump’s firing of James B. Comey, the former F.B.I. director, had been a breaking point for her. “Like a lot of people, I am appalled by the president’s conduct in office,” Ms. Barzee Flores said in an interview, adding: “I do believe that there’s a basis to impeach the president, and I do believe that he’s got to go. He’s dangerous.” But Ms. Barzee Flores said Democrats should not treat impeachment as a singular issue in 2018, over matters like health care and immigration. “There are other issues that are pressing,” she said. “More pressing, even.” a woman standing in front of a building: Mary Barzee Flores, a former circuit court judge seeking a Republican-held seat in Miami, said Democrats should not treat impeachment as a singular issue in 2018. “There are other issues that are pressing,” she said.© James Estrin/The New York Times Mary Barzee Flores, a former circuit court judge seeking a Republican-held seat in Miami, said Democrats should not treat impeachment as a singular issue in 2018. “There are…For Mr. Steyer, however, impeachment is a singular cause. And he is no easy character for Democrats to ignore: From his headquarters in a San Francisco office tower, Mr. Steyer, 60, has built a sprawling political operation with more than 200 staff members around the country, mostly employed by his flagship group, NextGen America, which focuses on climate change. Mr. Steyer has amassed a mixed win-loss record over the years, along with a mercurial reputation among Democratic strategists. But he is nearly alone among Democratic donors in his willingness to spend money on a titanic scale. In 2016, Mr. Steyer spent more than $90 million supporting Democrats, and his checkbook may be critical to their efforts to capture Congress. Separate from the impeachment drive, Mr. Steyer, who made his fortune as a hedge fund investor, announced this month that he would spend $30 million on mobilizing young voters in 2018. He has already quietly funneled nearly $2 million into a union-backed effort to capture seven Republican-held seats in California, three strategists directly involved in the campaign said. But on impeachment, Democrats in Congress have made no secret of their skepticism. Nancy Pelosi and Chuck Schumer, the Democratic minority leaders in the House and Senate, have called it a premature proposal. Senator Bernie Sanders of Vermont, a hero of the left, said Democrats should avoid “jumping the gun” on such a drastic action. And the Democratic Congressional Campaign Committee has urged candidates to use more measured language, endorsing investigations of Mr. Trump but avoiding an impeachment pledge. Ms. Pelosi, who has a longstanding relationship with Mr. Steyer and hosted him in her private box at the Democrats’ 2016 convention, conveyed her concerns to him directly. She told Mr. Steyer in a phone call last fall that impeachment was a profoundly divisive issue and stressed that other matters, like the Republican-backed tax overhaul, were more urgent, according to four people briefed on the conversation. But Mr. Steyer insisted that Mr. Trump had more than met the standard for being removed from office, and said his ads were electrifying the Democratic base. The conversation was cordial, according to associates of both Democrats, but neither gave ground. Mr. Steyer, his friends say, has been more pointed in private, appearing indifferent or even emboldened by the criticism of Democrats in Washington. Two of his friends, who spoke on the condition of anonymity, said Mr. Steyer has taken to declaring that when Ms. Pelosi or Mr. Schumer is complaining, he knows he is on the right track. But Ms. Pelosi and Mr. Schumer are not alone in their reservations. An impeachment resolution introduced last year by Representative Al Green, a Democrat of Texas, garnered only 58 votes in December. (When Mr. Green pushed for a vote for the second time in January, that number rose only slightly, to 66.) Even if the House did vote to impeach Mr. Trump — perhaps under possible Democratic control in 2019 — it would take a two-thirds vote of the Senate to remove him from office — a threshold that could only be met with the help of a sizable number of Republicans. That appears an extremely remote possibility. Representative Brendan Boyle, a Democrat of Pennsylvania who voted against the impeachment resolution, warned that pressing now could backfire badly. Voicing the exasperation of many of his colleagues, Mr. Boyle called the Steyer campaign a fruitless exercise. “I just don’t see how the ads achieve anything,” Mr. Boyle said. “To do this now, before Special Counsel Mueller finishes the investigation, only complicates our job if Mueller finds something that warrants impeachment, which I believe is a real possibility.” The Democratic base appears more receptive: Seventy percent of Democrats favor impeachment hearings, according to an NBC News/The Wall Street Journal poll published last month. Overall, 41 percent of Americans support impeachment hearings — an unusually high number for a president in his first year, but well short of an electoral majority. If Mr. Steyer’s focus on impeachment is new, his status as one of the most mercurial figures in Democratic politics is not. He has pursued a number of political adventures over the last few years, often hiring expensive consultants and spending heavily on advertising, and then abruptly moving on to an entirely new project. Last year, Mr. Steyer embarked on a kind of political star search, gathering national political strategists, including top advisers to Hillary Clinton and Barack Obama, to map out a run for governor or Senate. After briefly threatening to challenge Senator Dianne Feinstein, a fellow Democrat, Mr. Steyer abandoned plans to run for office in 2018. Former Representative Ellen Tauscher, a Northern California Democrat, said Mr. Steyer had plainly embraced a provocateur’s role instead of putting his name on the ballot this year. But Ms. Tauscher, who leads a “super PAC” targeting California Republicans, warned that voters might balk at electing a Congress bent on driving Mr. Trump from office. “You can’t have a conversation about impeachment until you take the House back, and so this is a little bit like somebody who’s jumped ahead,” Ms. Tauscher said, adding of Mr. Steyer: “I think, to a certain extent, Tom knows this.” Get updates about news across the United States via Twitter and in the Morning Briefing newsletter.