I have heard if you remove fees it will take a very very long time.
the only two times i've tried doing this, not on purpose it was a mistake, it went from 10 min, to 2 hours only, not a big deal
i never experience 1 day waiting or stuff like that
I never tried with zero fees as I'm not using bitcoin-qt or bitcoin core. In Multi-bit or Electrum it is not at all possible to send a transactions without any fees included. During the last stress test I was forced to wait more than 6 days for my transaction get picked even I set 11000 fees per kb.