There have been 73,441,399 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 five months of 2013 (2,495,440, 2,309,393, 2,209,407, 1,714,433 and 1,435,917 respectively) and the total number of background checks under President Obama comes to 73,441,399.
Since December 2012, when the gun sale surge hit its peak, background checks for gun purchases have slowly declined each month.