With Obama trailing in most national polls after the first presidential debate, Democratic hopes increasingly depend on a strong showing in the pivotal state of Ohio, where Obama maintains an edge. But it’s unclear whether Obama’s ahead a narrow or more meaningful margin.

Depending on your perspective, there’s a case that Obama leads by a modest margin or only a hair. The case for a slight Obama lead is straight forward: 6 of the 9 post-DNC polls show Obama leading by 1 point or less and a simple average of all 9 polls points toward only a slight Obama lead, with Obama ahead by just 1.7 points. Given the state's traditional Republican-lean and an impending surge in Romney ad spending, 1.7 points would hardly be insurmountable.

But there's also a case that Obama leads by a larger margin. None of the surveys show clear evidence of big movement in Romney's direction, and the tight race in post-debate polls might just be a product of the Republican-lean of many of the post-debate polls in Ohio. On average, Romney has gained just 1 point, which would suggest something like a 4 point Obama lead if the full suite of pre-debate pollsters weighed in on the Buckeye State and showed a uniform 1 point swing in Romney’s direction. As you can see, relatively few of Obama's best polls have surveyed the state since the debate.

Based on the data in Ohio alone, it's easy to see the case for Obama holding a 3 or 4 point lead in the state, rather than the 1 or 2 points suggested by a simple average of polls. The split between the polls also parallels methodological divisions, making it easier to argue that the other live interview pollsters will show Obama with a more comfortable edge. But it's harder to imagine Obama maintaining such a large lead in Ohio while methodologically similar surveys like Fox News, Pew, and Gallup show Romney ahead among likely voters nationally. And SurveyUSA found Obama leading by just 1 point despite calling cell phone voters. They didn't conduct a survey last month, but it seems hard to imagine that Obama wouldn't have led by a more substantial margin.