A hard but intellectually stimulating (and fun!) question. Maybe something like this:
-President: Leinad (L-GA)
-Vice President: TedBessell (I-CA)
- Secretary of State: Thinking Crumpet's Crumpet (D-WA)
- Secretary of the Treasury: Sparkey (L-CA)
- Secretary of Defense: LibertarianRepublican (R-FL)
- Attorney General: Torie (D-NY)
- Secretary of Commerce: North Carolina Yankee (R-NC)
- Secretary of Labor: Potus (R-WV)
- Secretary of Health and Human Services: ChairmanSanchez (R-FL)
- Secretary of Housing and Urban Development: ElectionsGuy (I-WI)
- Secretary of Energy: Enduro (L-PA)
- Secretary of Transportation: cxs018 (O-MA)
- Secretary of the Interior: Haslam2020 (R-TN)
- Secretary of Agriculture: evergreen (S-DE)
- Secretary of Homeland Security: ClarkKent (R-CT)
- Secretary of Education: PiT (R-CA)
- Secretary of Veterans Affairs: Dead0man (I-NE)
- Chair of Federal Reserve: Goldwater (R-WA)
- Chief of Staff: Adam Griffin (D-GA)
- Ambassador to the United Nations: CrabCake (O-UK)
- Press Secretary: Kalwejt (S-PL)
- CIA Director: Cathcon (R-MI)
As Smilo said, this is just quick and fun. Lots of good names I left off, too. I tried to have all of the positions make sense (e.g. a lawyer at AG, someone who has made many travels across the globe at SoS, etc.), although some links are a bit more tenuous (e.g. evergreen at SoAg--"green" as in plants and stuff
) and some I just kind of plopped in with little rhyme or reason. I obviously gave it a libertarian bent, but I tried to be ideologically diverse as well.