Michael Moore, the gadfly documentarian who has made a career out of fighting against conservative issues, has called for US citizens to stand up to President Barack Obama and back a court case he says is fighting a dangerous erosion of civil liberties.

The case has been brought against a little known piece of legislation called the National Defence Authorization Act (NDAA), which critics say has been changed to grant Obama the power to indefinitely detain American citizens without charge.

A group of activists, including Daniel Ellsberg – the official who leaked the Pentagon papers about the Vietnam war – and former New York Times journalist Chris Hedges have gone to court to get the language of the NDAA changed. On Wednesday an appeals court in New York heard arguments in the case and is set to render a judgment in the coming months.

Now Moore has come out swinging against the NDAA, too, saying that the White House is embarking on a plan to scrap vital civil rights that should concern every American citizen – despite a relative lack of publicity about the case. "At the moment a lot of people think the NDAA does not look scary. But this sort of thing never looks scary at the start. But the American people will rue the day if they do not stop this," he told the Guardian in an interview.

Moore was speaking after a court in New York heard an appeal in the case against the NDAA. Lawyers seeking to overturn the NDAA argued that it erodes American rights and free speech, and grants huge and unconstitutional powers to the government to suppress dissent and indefinitely detain people without going through proper legal channels. Lawyers for the Obama administration insist that the NDAA represents nothing new and has never been used in the ways that its critics suggest.

Moore said he would be seeking to explain the case to his fans. "If the American people understood this, I do believe they would be very, very concerned about it," he said. The force behind such hard-hitting documentaries as Fahrenheit 9/11 and Bowling for Columbine – which took on rightwing issues like President George W Bush's security policy and gun laws – said that liberals were giving Obama a free pass due to his popularity with Democrats. "[Obama] puts this face on it that makes it difficult. It was much easier when the face was Bush," Moore said "We have to work and speak out against the Obama administration and everything they are doing to destroy civil liberties."

Such strong language from a liberal icon is likely to shock many of Moore's usual audience. But the case brought against the NDAA is rapidly becoming a rallying cry for many civil liberties advocates, who see Obama as pursuing much of the same national security policy as his predecessor. "The major assault by the Bush administration has been embraced by the Obama administration," said Hedges.

The NDAA case hinges on language that critics say is too vague. It grants the power of detention and the right to use force against anyone deemed to have "substantially supported" al-Qaida or the Taliban, or "associated forces that are engaged in hostilities against the United States or its coalition partners". Critics say those terms are so broad that it, for example, include journalists or academics who interview Islamic militants or clerics. Or that the definition of terrorism might extend to those involved in projects like WikiLeaks or cyber-hacking groups like Anonymous or the Occupy protests.

Lawyer Bruce Afran, who is arguing the case in court, said that the NDAA laid a basis for massive future abuses, even if it currently was not being used in that way. "I know that the government is not setting up internment camps for journalists and activists," he said. "But the very fact that this power exists is what diminishes free speech."

Last September Judge Katherine Forrest surprised many observers by agreeing with the claimants and striking down the NDAA language as unconstitutional to free speech rights. However, the Obama administration immediately made an emergency appeal of the ruling and said Forrest's ruling did "irreparable harm to national security". An appeals court then stayed the decision and ordered the new hearings to be held on Wednesday. Eventually the case could go all the way to the supreme court.

Government lawyer Robert Loeb argued in the appeal that critics had fundamentally misread the NDAA and that journalists, activists and others had no reason to fear the law as it was not aimed at them. The Department of Justice also brought in testimony from three conservative Republican senators - Kelly Ayotte, Lindsey Graham and John McCain – to bolster their position. However, the lining up of such famously hawkish political figures on the same side as the Obama administration is enough to make people like Moore even more implacable in their opposition.

"By and large politicians are not tuned in. Perhaps Obama needs to just be educated about this issue," he said.