Polls show Mitt Romney and President Obama in a dead heat, but both campaigns are claiming they have the momentum in the rundown to election day. Team Romney is trumpeting its gains since the first debate, especially among women and in swing states. Obama's side says early voting is giving the president a bigger lead than expected in Ohio, a make-or-break swing state. The key question: Which campaign has the sort of edge that could really make a difference? Here, five arguments:

1. Romney's swing-state surge is what matters

Obama's cheerleaders in the media are loathe to admit it, says John Hinderaker at Power Line, but "swing state voters have moved into Romney's camp." The latest Rasmussen survey shows Romney with a "steady four-point lead" — 50 percent to 46 percent — in the battlegrounds that will decide the election. Romney's holding "blowout" campaign rallies in places like Red Rocks, Colorado. Even The Des Moines Register, "a Democratic paper," is contrasting Romney's optimism with Obama's negativity. It's clear which way the wind's blowing.

2. Romney had the momentum, but it's faded

"Romney clearly gained ground in the polls in the week or two after the Denver debate," says poll guru Nate Silver at The New York Times, "putting himself in a much stronger overall position in the race." His surge is over, though — in Wednesday's national tracking polls, he gained ground in one and lost a bit in five. "In other words, we can debate whether Mr. Obama has a pinch of momentum or whether the race is instead flat, but it's improbable that Mr. Romney would have a day like this if he still had momentum."

3. Actually, Obama leads where it counts

Two fresh Ohio polls "show President Obama stubbornly clinging to his electoral advantage," says Joe Scarborough at Politico. Both the TIME and NBC News/Wall Street Journal/Marist surveys showed Romney trailing the president by five percentage points in the Buckeye State. That's got to "rattle the nerves of Romney supporters" because the campaign's internal polls show a dead heat. If these polls are accurate, "Romney will have to grab most of Ohio's remaining undecided voters if he wants to win this critical battleground state," which could be the one that tips the Electoral College scales.

4. Romney's gains among women change the swing-state math

But other recent polls show Ohio in a "virtual tie," says Ed Morrissey at Hot Air. Why? "Romney has knocked six points off of Obama's 2008 gender gap and turned an eight-point deficit among independents into an eight-point advantage." Obama's 2008 "rock-star vibe has utterly faded." Meanwhile, Romney is clearly rising in the estimation of just about everybody still trying to decide. It appears "the magic has already shifted to Romney."

5. But Obama's crushing it in early voting

"No one pretends that Romney's ground game is anything close to what the Obama campaign has put together," says Ezra Klein at The Washington Post. Conventional wisdom says that could be worth 2 percentage points in the polls — the difference between winning and losing in a race this tight. Consider reports that "the Obama campaign is meeting and exceeding its early voting targets," giving him a "huge lead" in actual votes in Ohio, Arizona, and other key places. (In Ohio, for instance, a Time poll of early voters show them supporting Obama over Romney, two to one.) Obama is voting early himself Thursday, to inspire more people to do the same. "The Obama campaign's capacity to turn out its voters" early could be a big factor, says J. Robert Smith at The American Thinker. So Republicans cheering Romney's polling momentum might want to "put the cork back in the champagne."

Read more political coverage at The Week's 2012 Election Center.