if the founding fathers had wanted such a system, they could have easily stated as much and voting could have spanned many months by mail. however, they didn’t. they specifically wrote that elections should take place on a single day each election year. they were much wiser than modern citizens realize. they understood that voting was a responsibility and that elections should not be trivialized.
http://www.newsmax.com/BradleyBlakeman/Constitution-early-voting-election/2012/10/10/id/459517/
Article II, Section 1.
The Congress may determine the Time of chusing the Electors, and the Day on which they shall give their Votes; which Day shall be the same throughout the United States,.
http://www.archives.gov/exhibits/charters/constitution_transcript.html
Actually they specifically stated the states should appoint their electors however they saw fit and there doesn’t even have to be voting.