"What are you saying?" the president replied. "The notion that we are creating a plot to take everybody's guns away so that we can impose martial law is a conspiracy. Yes, that is a conspiracy. I would hope that you would agree with that."
It may be just a conspiracy theory, but Cooper was right that many people think mass gun confiscation is possible. And by dismissing this view so quickly, Obama might have actually increased its appeal.
In a poll conducted by the New York Times and CBS News in October, 52 percent of respondents said it was at least "somewhat likely" that "stricter gun laws will eventually lead to the federal government trying to take away guns from Americans who legally own them."
CNN conducted two surveys of gun owners in 2013 on this question. In January of that year, a narrow majority of gun owners -- 53 percent -- said they felt the federal government was trying to take away their right to own a firearm. In April -- after Obama and Vice President Biden had spent several months fruitlessly trying to convince Congress to expand the background-check program -- that figure had increased to 62 percent.
Those figures show why Obama's sharp words to Cooper on Thursday night might have been counterproductive.
"His response is very dangerous," said Joseph Uscinski, a political scientist at the University of Miami. "The term 'conspiracy theory' is one that’s often used to delegitimize your opponents, and it's a very dangerous term."
That's because one reason that people believe in conspiracy theories is that they already think they are politically marginal, that they lack power and legitimacy in the public sphere.
With his colleague Joseph Parent, Uscinski examined letters sent to the editor of the Times since 1980. They found that, when a Republican was in the White House, the conspiracy theories espoused by the writers had Republican and corporate villains. When the president was a Democrat, the villains were communists and Democrats.
In other words, people tend to believe conspiracy theories when they feel like they're losing. Fully 79 percent of Republicans and Republican-leaning independents say their side loses more than it wins in politics, according to a recent poll by the Pew Research Center, compared to 52 percent of Democrats and Democratic-leaning independents.
Whether Republicans really do lack political power is another question.
"They control the Senate. They control the House. They control a lot of state governments and governors' mansions," said Kyle Saunders, a political scientist at Colorado State University. Indeed, Republicans hold 68 out of 98 partisan state legislative chambers, more than ever before in GOP history.
That broad political representation is one reason that it's difficult to conceive of a mass gun confiscation by the federal government. Confiscation is a much more radical gun-control policy than the bill to expand an existing background-check program for people who want to buy guns, which failed in Congress in 2013 due to opposition from gun-rights advocates. Even if Congress did support it, confiscation would be unconstitutional. The Supreme Court has ruled that Americans have a right to keep handguns at home.
There also are practical reasons that gun confiscation on a large scale is highly improbable anytime in the foreseeable future. Since there are at least 310 million civilian guns in the United States, it isn't clear how the government would go about collecting them all, particularly if their owners didn't want to give them up. When Australia instituted a mandatory buy-back program to encourage residents to cooperate with a new law banning certain types of weapons, the government paid owners about $360 a gun -- and that was two decades ago. Since there are so many guns in the United States, a similar buy-back program here would be outrageously expensive.
But all the same, many Republicans seem to have a feeling of powerlessness.
"It's just the idea that President Obama is a Democrat," Saunders said. And his comments about guns could exacerbate that feeling.
"What he's really trying to say is 'Those people are crazy, they shouldn't be listened to, they have nothing to add to this conversation," Uscinski said. "That's not healthy, for a president to dismiss a large group of people as nuts."
Guns are a way that those who fear Obama and his policies can feel like they have a measure of control over their own situation. Advocates for gun rights often claim that weapons will be needed so that citizens can fight back against the federal government, and sales of guns have skyrocketed since Obama took office.
"It's about power," Saunders said.
If firearms represent power, then they are also a symbol of the very thing that people who endorse conspiracy theories feel they lack. It wouldn't be surprising if people with conspiratorial tendencies bought more guns or if they were particularly anxious about the chance of losing them. And Obama's refusal to acknowledge those anxieties might just increase his audience's feeling of powerlessness.
Scott Clement contributed reporting.