There have been 72,005,482 background checks for gun purchases since President Obama took office, according to data released by the FBI.
In 2009, the FBI conducted 14,033,824 background checks. If we subtract the month of January (Obama did not assume office until the end of the month) we get 12,819,939.
The FBI conducted 14,409,616 background checks in 2010, 16,454,951 in 2011, and 19,592,303 in 2012.
Add to that the first four months of 2013 (2,495,440, 2,309,393, 2,209,407 and 1,714,433 respectively) and the total number of background checks under President Obama comes to 72,005,482.
Obama has been President for 1,550 days. That works out to 46,455 background checks for gun purchases each day.