Will Unemployment Factor into the Presidential Election?

President Obama recently stepped into some political hot water when he described the private sector economy as "doing fine," which caused Governor Mitt Romney to ask if he was out of touch.  President Obama was speaking at a press conference on the European debt crisis, and was referencing private sector versus public sector job creation.  It hardly matters in the world of politics, but on the matter that he was speaking, he was correct.  While I don't have jobs numbers, private consumption as a component of real GDP is up 1.9%, private investment is up 0.81% and it is government consumption that has become the current drag on real GDP with -0.78% in the first quarter of 2012 (Bureau of Economic Analysis).

The real story in the U.S. is still unemployment, which has not been fine for three years now. The current unemployment rate is 8.2%.  Will this persistently high unemployment cost President Obama a second term?

Nate Silver is a statistician with the New York Times who is famous for predicting 49 of 50 states in the 2008 Presidential election and all 35 Senate races.  On his website, he is stating that President Obama has a 62.6% chance of winning.  He also notes which states are most contestable; and because of our electoral system, those outcomes are the most important.
Will any potential changes in the unemployment rate because of Europe or an overall weakening American economy affect the upcoming election?  Here are some maps of key states (according to Mr. Silver) along with their unemployment rate difference year over year from April 2012.  Darker colors are improving unemployment numbers; click on the maps for greater detail.

Bureau of Labor Statistics

Mr. Silver is predicting Virginia, Ohio, Colorado, and Nevada to be won by President Obama.  He is predicting Florida and North Carolina to be won by Governor Romney.  Nevada and Ohio are especially looking like they are experiencing pretty significant job slumps in the past year or so, but will that matter?

I ran regressions on previous election years to see if it has mattered in the past.  They showed little correlation between difference in the three month employment change, or the unemployment rate generally and incumbent party win or loss.  With the year over year change in unemployment, they did show a r = 0.3734 which is still pretty weak, but much better than the other two.

These correlations are very low, and some basic transformations that I attempted did not help their r's at all.  It does seem that election year changes in unemployment have had a low impact on imcumbent election outcomes since 1948.  This is likely due to the multitude of different factors that voters must evaluate potential Presidents based on.  Many years economic factors are not even the most important ones.  Could this also be evidence supporting Bryan Caplan's idea about the myth of the rational voter?