Sherlock Holmes would be very analytical and Holmes could be his VP, so that might not be so bad.
Jessica Fletcher, AKA Angela Landsbury, would not put up with any nonsense while giving you a sense of fuzzy grandmotherly comfort. Jackie Chan’s Chon Wayne and Owen Wilson’s Character from Shanghai Nights & Noon, I think would be a good combination of Honor, discipline, zen-metaphyscial BS and slo-mo pillow fights that congress is in desperate need of having.
Senator Jefferson Smith. Though he might need Senator Joseph Harrison Paine as his V-P to keep him in touch with some aspects of reality. (I know, the US Constitution wuld not allow them to be Pres and VP, but it would be a goiod combination).
I’d love to see Justin Foote, of Heinlein’s Time Enough For Love.
Lazarus Long would be great too, but he’d never take the job.
Others:
Jack Ryan of Tom Clancy’s novels. He does a great job in the books, anyway.
Jack Sawyer from Stephen King/Peter Straub’s The Talisman and Black House.
And I would think that Gordon Dickson’s The Final Encyclopedia and the Dorsai series contain several great fictional presidents, especially Donal Graeme, Hal, and Bleys Ahrens. Ahrens would be great, although probably wouldn’t do too much on social issues and welfare…