Well... The upper bound is
9, because California must be included in the winning configuration, and 538/55 = 9.
Here is one potential solution
CA(55)
TX(38) + NJ(14) + AK(3)
FL(29) + IL(20) + AR(6)
NY(29) + PNPA(20) + IA(6)
OH(18) + GA(16) + VA(13) + KTKY(8)
MI(16) + NC(15) + WA(12) + AL(9) + DADE(3)
AZ(11) + IN(11) + MA(11) + TN(11) + KS(6) + NM(5)
MD(10) + MN(10) + MO(10) + WI(10) + CO(9) + MS(6)
SC(9) + LA(8) + CT(7) + OK(7) + OR(7) + NV(6) + UT(6) + WV(5)
With all other Electoral votes going to tenth or lower places. The top three electoral vote receivers are then supposed to go to the House of Representatives to be decided... good luck to them.