If "not much less than water" means "not an order of magnitude lower than water at room temperature" this is probably correct. However there are substances like http://en.wikipedia.org/wiki/Pentane with a viscosity 4 times less than that of water or http://en.wikipedia.org/wiki/Acetone with a viscosity 3 times less than water (at 20 degrees celcius). At lower temperatures (77K) you find liquid nitrogen with an viscosity less than 5 times that of water at room temperature. On the other side at 1K helium becomes a superfluid with effectively zero viscosity http://en.wikipedia.org/wiki/Superfluid_helium-4) In that sense viscosity seems to behave similar to electric resistance, being lower with lower temperature. So without reading Weisskopf I guess it's simply room temperature which provides an lower limit to the viscosity of a fluid.
asmaier
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