The result of all this is that, as Yale political scientist John Bullock puts it, the media is “going to have a very hard time trying to persuade Republicans that a particular attack on Obama is false, no matter how good a job they do, and vice versa.” And there’s another wrinkle to the problem, Bullock said. Research suggests that even if a specific factual misunderstanding can be refuted, the judgment it facilitated is likely to remain. In other words, even if the idea that the government wants to create “death panels” is discredited, the suspicion of health care reform that the belief fostered will linger.

That’s discouraging news for Obama’s health reform ambitions—but it’s also pretty disheartening for the press, which counts as one of its core responsibilities the communication of accurate information about the world, with the expectation that that information will inform public debate. The media itself, of course, is often culpable in spreading misinformation. But if people, at a certain point, aren’t listening, are even good journalists—the skeptical, truth-telling sort, who challenge authority, check the claims they report, and speak truth to power—really communicating?

Nyhan, for one, is not quite ready to despair, and he continues to urge the media to do a better job of policing misinformation. On his blog, he criticizes newspapers for offering weak objections to political inaccuracies—he was critical, for example, of a recent New York Times primer on the health care debate that said only that the euthanasia claims “appear to be unfounded.” There’s no evidence that a more forceful fact-check would be more effective in refuting false claims, Nyhan said, but “I hope that they would [do so anyway]—it might provoke a stronger response.” (He added, though, that that response might diminish the press outlet’s credibility in the eyes of some readers.)

An even better press strategy, he believes, is “naming and shaming”—calling out the people who help falsehoods advance, and cutting them off from media access. Such an approach might not change minds on a particular issue, Nyhan said, but it would “increas[e] the reputational costs” of spreading lies, and thus create a climate in which truthfulness and accuracy were more prized.

This approach may bear fruit, but it has a few potential weaknesses. One is that major media outlets are not the gatekeepers they once were. Another is that the strategy presumes a level of coordination that doesn’t exist within newsrooms, let alone across the industry. When an ABC News reporter, for example, sets out to shame former New York Lt. Gov. Betsy McCaughey for her role in advancing the euthanasia myth, there’s no reliable way to ensure that others follow suit—or even, for that matter, see the story. And a third is that some people who foster misinformation—for example, sitting Senators who are at the center of ongoing negotiations on health care reform—can’t really be shunned.

So where does all this leave the individual reporter, working on a specific story for a general audience, who wants to debunk a false statement made by a subject? “The best chance,” Schul said, “is to tell a good story—you want to create a causal chain that links the new information to evidence the perceiver already knows so that it can modify the old interpretation [with] the one you wish to implant.” Nyhan suggested another idea: find someone who’s ideologically similar to your target but willing to repudiate the claim, as conservative Republican Sen. Johnny Isakson recently did on the euthanasia story. But such white knights are not always available, and when it comes to the other instances, “I’m at a bit of a loss,” Nyhan said. “We don’t have micro-level evidence about how to frame these stories.”

Greg Marx is a CJR staff writer. Follow him on Twitter @gregamarx.