Is it OK to drill one or two 2 inch holes into a load bearing header in my basement?
While your local building codes may vary somewhat, please refer to this IBC document section on &quot;Notching and Boring&quot; of load bearing members:
Notching and Boring Standards
According to section R502.8.1, you can bore a hole up to 1/3 the width of the member as long as it is not closer than 2&quot; to either edge of the member.  Also note that you cannot bore or notch engineered beams unless you have the modifications to the beam certified by a qualified and registered engineer.
I would proactively check with your local AHJ (i.e. building code compliance office) so that you are aware of any differences they may have from the IBC.  That will help you a lot when the time comes for the inspector to pay you a visit and sign off on the work.