Yes, it turns out that there is a body of research from political scientists about the electoral effects of extreme weather events. John Sides summarizes it over at The Monkey Cage. Basically, it comes down to two major effects: on the one hand, people tend to penalize incumbent politicians for bad weather, irrational as that might seem; on the other hand, they tend to reward politicians who are perceived to have responded well to major storms.
All that would presumably apply directly to those in the storm path; John also notes the effects of the disruption of early voting in swing states Virginia and North Carolina. What about effects on the rest of the nation?
For the overwhelming majority of voters who have already made up their minds, any significant effects at all would be surprising. For the small remaining group of undecided voters, what could matter quite a bit is the information environment in the last several days of the campaign. Normally, we would expect it to be more or less even: both candidates would have strong sound bites on the news from massive rallies of enthusiastic supporters, and any charges or counter-charges would be more or less equal. If it turns out that instead the information environment is (other than TV ads) not about the election or the candidates at all, then there’s no change — other than losing the possibility that some campaign even could dominate the news in the last few days.
On the other hand, if storm coverage winds up having a strong component of making the federal government response — and thus the president — look either particularly good or bad, then that definitely could have an effect around the margins on late-deciding voters.
The key is that for most citizens, what the campaign really does is to educate us to vote for the candidate we “should” vote for. If we’re partisans, we are reminded of what we like about our party; if we’re issue voters, we relearn which party cares about that issue; if we’re weak partisans with little long-term attachment, we might be swayed to vote for or against the incumbent party based on how we perceive things are going in the nation (and “learn” to like or dislike the out-party candidate accordingly).
However, for low-information late deciding citizens who have little attachment to politics, there’s often no “should” candidate. And as a result, such voters, if they vote at all, may be swayed by whether most of what they’ve heard recently about one of the candidates is strikingly good or bad. And with Sandy, it’s fairly likely that if there is any information about the candidates dominating the news, it’s either going to be Barack Obama looking good while running the federal response to Sandy — or looking bad running the federal response to Sandy.
But the main effects, again, are likely to be small — because most voters have already decided (or even voted!), and those voters are likely to interpret whatever happens through that decision.