Lawprof Michael Froomkin (Discourse.Net) had a great post last year on this subject; I missed it when it first went up, but it's still interesting now:
As my friend John Berryhill points out . . .:
[S]hadow cabinets have not been used in the United States because [a candidate who promises, as part of his election campaign, to appoint someone to the Cabinet] would face up to two years in jail under 18 USC § 599:
"Whoever, being a candidate, directly or indirectly promises or pledges the appointment, or the use of his influence or support for the appointment of any person to any public or private position or employment, for the purpose of procuring support in his candidacy shall be fined under this title or imprisoned not more than one year, or both; and if the violation was willful, shall be fined under this title or imprisoned not more than two years, or both."
Incidentally, I'm not sure that this provision is constutitional — see Brown v. Hartlage (1982). (Please don't argue in the Comments that it's constitutional or unconstitutional without having read Brown; it's both the most directly on-point precedent, and it makes important policy arguments that even people who don't care much about precedent should deal with.)