IN DAILY verbal broadsides, Brazil’s president, Dilma Rousseff, and her political allies claim that the attempt to impeach her is a “coup d’état”. It is an emotive statement that moves people beyond her governing Workers’ Party (PT) and beyond Brazil. Her supporters held rallies on March 31st, the same day that in 1964 Brazil’s army took power in the last actual military coup the country suffered. “We are here in unyielding defence of democracy,” Chico Buarque, a singer and writer, told the crowd in Rio de Janeiro.

Ms Rousseff argues that she has not committed a “crime of responsibility” and that her impeachment is therefore illegal. There is no evidence that she is personally corrupt. Unlike her lead accuser, Eduardo Cunha, the Speaker of Congress’s lower house, neither she nor her family have Swiss bank accounts or Panamanian offshore companies. Many of her would-be impeachers are accused of taking bribes in the scandal centred on Petrobras, the state-controlled oil company. The administrative crime of which she is accused—a piece of fiscal trickery—is a technicality, her defenders say.

Behind her impeachment they see the same de facto powers—the media, private business, prosecutors and judges—which, they claim, brought down democracy in 1964. Military juntas may be a thing of the past in Latin America, but Ms Rousseff’s allies point to a pattern of “soft coups” that ousted presidents of the left, in Honduras in 2009 and in Paraguay in 2012.

Denouncing supposed coups has become part of the left’s propaganda kit. Nicolás Maduro’s government in Venezuela constantly spies them, the latest in the form of a law granting amnesty to political prisoners. Last year Evo Morales, Bolivia’s president, warned of a “judicial coup” against Argentina’s then-president, Cristina Fernández de Kirchner, because a judge proposed to investigate her.

Those who cry wolf about coups take a selective view of democracy. Mr Morales seems to think that all courts should be an appendage of the executive, as they are under his government. Mr Maduro, who was elected in 2013 with 7.6m votes (50.6% of the total), denies all legitimacy to the National Assembly, which was won by the opposition last December with 7.7m votes (56% of the total). This is the perversion, not the defence, of democracy.

A coup involves the seizure of power through the unconstitutional use or threat of force by a small group. That is not the case in Brazil. Whatever their occasional slips, the corruption probe is run by independent prosecutors and judges. The constitution allows for impeachment, but only by a two-thirds majority in Congress.

Supporters of its use against Ms Rousseff argue that it is a political as well as legal matter—that is why the Senate, and not the supreme court, tries the case. They say that from 2003 PT governments installed an organised scheme of graft in Petrobras which funnelled money to the party and its allies with the aim of securing a permanent hold on power. Her fiscal misdemeanours qualify as a crime under the impeachment law. They are right that impeaching Ms Rousseff would be a constitutional act with a legal basis, albeit a flimsy one. In opinion polls, two-thirds of respondents are in favour. But that doesn’t make it wise: it would divide Brazil and risk poisoning its politics for years.

The drama the country must deal with is what to do when a government ceases to function. Ms Rousseff began her second term in January 2015 with the economy collapsing, along with her popular and political support. Each week brings fresh claims of corruption. The president does not govern in any meaningful sense of the term. The country cannot withstand almost three more years of this.

In parliamentary systems, the government normally falls under these circumstances. In presidential systems, such breakdowns are traumatic. Fortunately, the days when they triggered real coups in Latin America are past. But the underlying problem remains. Ms Rousseff has set her face against resigning, or seeking a government of national unity. Anyway, her vice-president signed some of the questioned fiscal measures and may now be impeached, too. If that happens, the best way out would be a fresh election.

The electoral tribunal may call one: it is looking at claims that money from Petrobras bribes financed Ms Rousseff’s campaign; her campaign guru has been arrested on those grounds (he denies wrongdoing). But Brazil also needs a new Congress, given its tainting by corruption. An early general election requires a swift constitutional amendment. Next time they take to the streets, it is what Brazilians should call for. That would be a better way to defend democracy.