The Queen of Soul sang for the pair - as well as for about 3,000 fans at DAR Constitution Hall on Saturday night.
After, Aretha said it was great to see her VIP guests relax and "shake their hips a little", especially after a tough re-election campaign.
Aretha has performed for Mrs Obama before - at the inauguration of President Barack Obama. Aretha added that she doesn't think there will be an encore in 2013, though if invited she "would certainly come and would love to sing".
The soul star also paid tribute to the late Whitney Houston, singing I Will Always Love You.