AMERICA has elected a man of frightening impatience as president. That is no reason for Donald Trump’s opponents to copy him. Four months into the Trump presidency his sternest critics seem ready to tear the country apart, just to see him gone. Democrats and activists on the left, including members of Congress, are already calling for his impeachment. They revel in leaks that batter the White House almost nightly and yearn for the wheels of justice to spin as fast. Their goal is a speeded-up Watergate, fit for an on-demand age. On the Trump-sceptic right pundits call the president a tyrannical “child upon the throne”. Some see the 25th Amendment to the constitution as a shortcut to adult supervision—just as soon as the vice-president, cabinet and a two-thirds majority in Congress agree that Mr Trump is “unable to discharge the powers and duties of his office”.

Leave aside, for one moment, the legal and political hurdles that could delay the impeachment or dismissal of Mr Trump for years, if not for ever. If opponents did somehow succeed in toppling him before most Americans are ready to endorse such a step, they risk splintering the same democratic order that they want to save. It is not enough to point to opinion polls that show public approval of the president slipping each week. Though pro-Trump sentiment is softening, the proportion of the country that is implacably opposed to him still falls some way short of a majority. A revealing poll taken in mid-May by YouGov—the CBS News 2017 Nation Tracker—found that 40% of Americans are convinced opponents of Mr Trump, while 19% of respondents are unwavering supporters and 22% will continue to back him if he delivers what they want. The final 19% would reconsider their dislike of Mr Trump if he “does a good job”. The poll contains a further ominous note: when the president is criticised, 79% of his supporters also hear an attack on “people like me”.

This is not to argue against investigating whether Mr Trump or his aides colluded with Russia, a hostile foreign power. If the president is guilty of high crimes, he must face the consequences. But impatient foes want him gone now, before millions of Americans have even started paying attention to Russian headlines. Rush this, and half the country may think their president has been stolen from them. America is not just more tribal than it was during Watergate: conservatives have spent years training their side to distrust anything the press says.

Still some Trump opponents would not wait. They say the president is a menace now, and see no merit in delaying the moment when his voters finally grasp that they are a demagogue’s dupes. Here is an alternative suggestion: take a deep breath, avoid hinting that Trump supporters are stupid, and let them work out for themselves that he is not very good at his job.

Happily, there are recent, real-world examples of patience working, and snarling populists losing office by outstaying their welcome. One of the most instructive involves Joe Arpaio, a law-and-order showman defeated last year as he sought his seventh term as elected sheriff of Maricopa County—a sprawling, sun-baked tract of Arizona that includes the city of Phoenix and is home to nearly 4m people. A concise explanation of Mr Arpaio’s defeat is that locals grew weary of his distracting antics, even if the sheriff was a star of conservative talk radio and TV.

Mr Arpaio, who styled himself “Sheriff Joe” and “America’s Toughest Sheriff”, was an authoritarian impresario. He housed county prisoners outdoors in tents, even as temperatures reached 145°F (63°C), made them wear pink underwear and put them in chain gangs. He recruited a posse of volunteer sheriff’s deputies, who sport police uniforms and roar about in patrol cars. When that felt old, in 2011 Mr Arpaio assigned a five-member “cold-case posse”, financed by conservatives across the country, to investigate whether Barack Obama had faked evidence of his birth in America. While lesser rivals acquired military hardware from the Pentagon, Mr Arpaio secured a tank (actually a self-propelled howitzer). He made the action film star Steven Seagal a posse member and let him drive that tank through a local man’s garden wall in search of illegal cockfighting. Sheriff Joe’s fans cheered when he ordered immigration sweeps that targeted people who appeared to be non-white or Hispanic. He was an early Trump backer, declaring: “Everything that I believe in, he believes in.”

Hey Joe

By 2016 many conservatives had stopped chortling. County taxpayers had by then paid tens of millions of dollars in legal fees and settlements for lawsuits against the sheriff’s department, including for prisoner deaths. Mr Arpaio faced charges for criminal contempt, after allegedly defying court rulings to stop racial profiling. The Pentagon asked for its hardware back after several weapons were lost. Amid this dysfunction a veteran Phoenix police sergeant, Paul Penzone, ran for sheriff as a Democrat and won. He did not call Arpaio supporters bigots. He told them that their money had been squandered and that law enforcement had suffered. That back-to-work message won Mr Penzone 158,000 more votes than Hillary Clinton received in Maricopa County, as he picked up support from Republicans who were either embarrassed by Mr Arpaio, or decided that he was a blowhard who bored them. Sheriff Joe’s gimmicks “weren’t doing it for him any more”, summarises David Berman, a political scientist at Arizona State University. At some point, “people say, can you do the job?”

As for Mr Trump, some will stick by him regardless. But others may conclude that the president is a do-nothing blowhard in his turn. That might open a path for a problem-solving Democrat to defeat the president in 2020. If Mr Trump’s poll numbers are bad enough Republican grandees might offer to carve his face on Mt Rushmore, if he retires without seeking a second term. Making Mr Trump a martyr could tear the country in two. Letting voters tire of him might be the least-bad outcome.