The problem is that "gains" or "losses" depend entirely on your frame of reference.
Bush: Entered office January 2001 when the number of Private Sector non-farm payroll jobs was at 11,631,000. This was a recessionary time period and until July 2003 there was an average change of -113,300 jobs/month for a total loss of 3,399,000 jobs.
But then recovery and from July 2003 to January 2008, the average change was +137,315 jobs/month for a total gain of 7,415,000 (just over 4 million more than when he took office).
But then things went bad again and from January 2008 to January 2009, Bush's last year, the change in jobs was an average of -388,500 jobs/month for a loss of 4,662,000 and a net change of -646,000 when he took office.
So did Bush gain or lose jobs? Both. It was lose 3.4 million in 30 months, gain 7.4 million in 54 months, lose 4.7 million in 12 months.
Similarly, under Obama, we were already losing jobs severely (-4.7 million in 2008) and things kept going. From January 2009 to February 2010, the average change was -324,000 jobs/month for a loss of 4,212,000 (on top of the 4.7 million already lost during Bush's last year).
But since February 2010, things have improved (and Obama is sure to use Feb 2010 as his reference point) where the average change has been +156,143 jobs/month for a gain of 4,372,000
So under Obama it's been: Lose 4.2 million in 13 months, gain 4.4 million in 28 months.
So which period of gains or losses you choose, and how you twist the comparisons is all up to politics. Obama, of course, likes to emphasis the 4.6 million lost under Bush and the 4.4 million gained in the last 28 months and ignore completely the 4.2 million jobs lost under him as an extention of the losses under Bush.
All numbers derived from
http://data.bls.gov/pdq/querytool.jsp?survey=ce and refer to seasonally adjusted private sector jobs.