Here's what the WSJ found back in March: "[O]ver the past year the price fluctuation has just been from $10.001 to $10.000, even amid the European crisis, debt ceiling debate and Standard & Poor's downgrade of U.S. government debt."
This is likely going to be the experience of the overwhelming majority of funds that would float their NAVs. Any deviations from the target NAVs would likely be so small as to be statistically insignificant—at least for retail investors who don't have enough money tied up in the funds such that infinitesimal fractions of a cent would make a difference.
Ultimately, at least in the short term, fund providers and other members of the financial industry are right to fear that a floating NAV would lead to outflows. But in the long term, there's reason to believe—or at least hope—that investors would begin to accept the fluctuations for what they really are: blips on the radar.