Yes, you do need one for overnight... but I have never had an issue getting one.
IF you want a more challenging alternative to Whitney, Williamson and or Tyndall from Shepherds Pass are worthy and butt-kicking alternatives.
Of the CA 14'ers, the only ones I haven't climbed are the Palisades from Sill to Thunderbolt, but I think Tyndall is my favorite 14er summit. Middle Pal is a close second.