It seems like a bizarre question to ask. Why would voters punish Obama for a severe drought across the United States? The president can be plausibly blamed for lots of things, but a hot, parched summer seems like a bit of a stretch. (Even if climate change is contributing to the current drought, the Obama administration has at least taken a few steps to rein in U.S. carbon emissions, after all.)
And yet, some political science research suggests that natural disasters like droughts and floods really can hurt an incumbent president. A classic 2004 paper (pdf) by Christopher Achen and Larry Bartels looked at U.S. data on flood and droughts throughout the 20th century and found that "voters do indeed punish the incumbent party at the polls for presiding over bad weather." It may be irrational, but it happens far too frequently to be a mere coincidence.
In one striking example, Achen and Bartels looked at the 2000 contest between Al Gore and George W. Bush, which took place after a period of severe droughts across the South and West, as well as flooding in the Dakotas, New York, and Vermont. The authors ran a number of regressions and concluded that droughts and floods may well have cost Gore up to 2.8 million votes across the country. Over at the Monkey Cage, Bartels offers up a graph:
And yes, it would be ironic if the type of droughts and floods Gore has long warned that global warming will bring actually cost him the White House in 2000. (Of course, for this effect to be decisive in a presidential election, the drought unhappy voters have to be in swing states.)
The drought effect isn't all that unusual. Achen and Bartels assemble a variety of evidence that voters punish incumbents for all sorts of "acts of God," including, famously, the 1916 shark attacks in New Jersey which appear to have cost Woodrow Wilson votes. They do caution, however, that this doesn't always happen. The 1918 Spanish flu, which killed nearly 500,000 people in the United States, didn't seem to unleash an anti-incumbent wave.
It's a bit of a mystery why certain natural events hurt incumbents and others don't. One possibility is that the government reaction to an "act of God" can make a difference. A 2011 paper (pdf) in the American Journal of Political Science found that found that the electoral benefits of a competent response to natural disasters can be pretty significant and last for years. The caveat? This study looked at a 2002 flooding event in Germany, not the United States.
In any case, here's Bartels: "Do voters really expect President Obama to make it rain? Probably not. But that won’t prevent them from punishing him if it doesn’t. When conditions are hellish, policy discussions are likely to be less edifying than expressions of frustration."
Update: And here's another study, from Boston University's Andrew Reeves, finding that while American voters can and often do punish incumbent politicians for natural disasters, the response to disasters can make a big difference. To wit: "We find that electorates punish presidents and governors for severe weather damage. However, we find that these effects are dwarfed by the response of attentive electorates to the actions of their officials."