I found a fair bit to like in Politico’s latest conversation-driver, a long article by Jim VandeHei and Mike Allen on the daunting re-election prospects faced by President Obama. The story appropriately puts the foundering economy atop a list of obstacles facing Obama, and it offers a sharp discussion of how the changing landscape of campaign finance might mean Obama’s apparent advantage there isn’t as strong as it now seems.

But this discussion, which appears under the subhed “Independent Angst,” repeats some unfounded conventional wisdom that really should have been beaten out of horse race coverage by now:

Even in good times, Obama would have a tough reelection. The 2008 election—featuring a weak GOP candidate, in a terrible political environment for Republicans—obscured the inescapable fact of modern politics: This is a 50-50 nation, controlled at the presidential level by independents.

Obama gets this. There is a reason he shifted so quickly to being a Bill Clinton centrist after the 2010 congressional defeats. He knows the key to reelection is winning back the independent voters who helped elect him—and then bolted in the face of his health care push. It helps explain why after largely ignoring debt in the first two years—then again after his own debt commission offered a clear path in November, then again with State of the Union speech, then again with his first proposed budget for next year—he became the champion of a $4 trillion debt reduction plan. It’s called survival politics.

He entered office with 62 percent support among independents. But they took flight in the spring of 2009—and have never returned. Those voters helped Republicans win the off-year gubernatorial races in New Jersey and Virginia, now-Sen. Scott Brown’s race in Massachusetts a few months later, ultimately control of the House—and, more important but less talked-about, many state legislatures around the country.

There may be a germ of truth to this. Based on the current outlook, if Obama does win re-election, it will likely be by the barest of margins. In a context where the outcome may hinge on fractions of a percentage point, things that don’t usually matter much—e.g., political “messaging,” state-by-state swings—may start to. (As CJR favorite Brendan Nyhan told Adam Serwer for a smart story in The American Prospect, for this reason close elections are “nirvana” for pundits.) And maybe—maybe—Obama’s centrist positioning will be a modest asset for him in the coming campaign.

But the broader claims here—in particular, the idea that independents “control” presidential elections—have been undercut by ample research, some of which Ruy Texeira summarized just this week in a column for The New Republic. The main thing to remember, as Texeira notes, is that independents are not a cohesive group: about two-thirds of Americans who call themselves independent lean toward one party or the other, and it turns out that they vote just like people who self-identify as partisans. Further, “pure” independents vote less frequently than other adults, which makes sense—if you truly don’t have a preference between Democrats and Republicans, it’s probably because you’re not very politically engaged. Add it all up, and in 2008 only 7 percent of voters were pure independents.

Seven percent is still plenty large enough to determine election outcomes in a “50-50 nation,” of course. But that gets us to the other flaws with this line of analysis. As John Sides wrote last fall at The Monkey Cage, even pure independents don’t seem to be moved by presidential attempts at bipartisanship or centrism. Instead, their votes are influenced even more strongly by the economy than are other voters’. (Again, this makes sense: most Democrats will almost always vote for the Democrat, and likewise for Republicans, regardless of the economy.) So all the “survival politics” Obama can practice probably won’t improve his standing among this group if the economy doesn’t somehow rebound.

Greg Marx is an adjunct lecturer at The Medill School and a facilitator with The OpEd Project. She served as an editorial board member, columnist, library director, and No. 2 in the features department of the Chicago Sun-Times.