Peter Baker wrote an article in the NY Times in May talking about how the American public loves to compare Obama to past presidents.
When his poll numbers are up, he's been compared to Abe Lincoln and Thomas Jefferson. If he addresses the American public directly, bypassing Congress, he's been called our generation's JFK or Regan. When his numbers are down, he's been called the next Carter or LBJ.
However, this isn't really a new phenomenon. When Rutherford B. Hayes was asked to perform one of Washington's speeches on the founding of the Republic for America's centennial in 1876, he was roundly criticized as a symbol of how far the country had declined.
Andrew Jackson (Old Hickory) was sort of a Regan type figure of his times, a divisive politician that enjoyed great loyalty and respect from some segments of the population and was reviled by others. His later admirers who would go on to become president were James Polk and Franklin Pierce. Both their supporters and opponents jointly gave them the nicknames 'Young Hickory' and 'Young Hickory of the Granite Hills' respectively to highlight the common policy of the three men.
Abraham Lincoln's supporters commonly compared him to George Washington and Thomas Jefferson for both his reputation as a warrior struggling to save the country and a man of peace. This was somewhat strange since the Confederate President Jefferson Davis was also commonly compared to Thomas Jefferson by his supporters for his belief in states' rights (to own slaves).
George W. Bush has been compared to James Polk for his partisanship and his skill at ramming through legislation, making enemies but also achieving his ambitious political goals.
Even George Washington in his own day was compared to a figure from history when there were no other presidents to compare him to. Washington was given the name 'Cincinnatus' after the Roman retired general/farmer who quit his plow and took his sword back up to defend his country from foreign invaders.
Maybe it's just human nature that people treat history like baseball, always looking for comparisons of current and former greats. At some point though, we have to accept that before they're anyone else, presidents are themselves, making their own history.