Yes, you could… theoretically
Q: How can I get a job in the Obama administration? — Job-seeker
A: They do seem to be the only ones hiring, don’t they?
For high-level positions, it helps to be a former candidate for the Democratic nomination; a governor or senator who plays well with people on both sides of the aisle; or a senior staffer on the Obama campaign. Come January, it might help if you’re a hypoallergenic puppy in need of a good home.
The rest of us can apply via change.gov. According to the confirmation email I got, the administration will keep applications on hand well after the election – so even if you don’t get an administration job, you could still put “considered for position in Obama adminstration” on your resume. It’s a better talking point than your certificate in some technology that hasn’t been applicable since 1996.

People ask me stuff. I answer, if I feel like it. Pretty straightforward, really.