how can low watt tube amps drive speakers with higher power requirements

My favorite  design is a pair of NOS 300B tubes operated in single-ended, ultra-linear mode. About 15 watts RMS output.

Funny!!! 300bs of course can't be operated in ultralinear, on account of lacking a screen grid :)

I read that certain speakers require amplifiers with high "current" and not necessarily high wattage.....and this usually requires a tube amplifier. I believe this has something to do with 20w tube amplifiers driving speakers better than a 150w SS amplifier.

Indeed, wattage is just part of the equation.. Average watts per channel RMS (root mean square) is an average which means there will be peaks and valleys of  power output way beyond and way below the RMS value.  Amplifier manufacturers that do not state power in watts RMS per channel is quite meaningless or hard to understand what they mean.  And the quality of the first watt is super important.  For instance, Klipsch Heritage speaker line with efficiency up in the 98 and above can easily be powered by a 2.3 watt/ch  SET amplifier from Decware (see Steve Guttenburg's YouTube channel on this very topic) if you listen at a relatively reasonable level (vs a night club !).  There is an obsession on the more watts, the better. That is not necessarily true.  PLUS, some speakers have impedances that are all over the map and can approach zero ohms (e.g. almost a short circuit)  and that requires a very well designed amplifiers (e.g. David Berning's)  more than just powerful amplifiers.  

No you are not missing anything. You can get to a fairly high static output with a low powered amp on a less efficient speaker .....playing a sine wave. Music is not static. It is very dynamic. Peaks can require 10 times the output or more. Thus at volume the amp is clipping all the time and the sound is pathetic. If you only listen at very low levels it will work. I love string quartets but I could never spend my whole life listening only to them. Replace the amp with a very powerful one, 200+ watts/ch and music flows out of the speaker in an effortless and dynamic fashion. For low powered amps you have to stick with very efficient speakers but IMHO anything less than 30 watts/ch is a waste of time. Unless you only listen to string quartets. You can get SET amps this powerful if you feel the need. They are also stupid money. For less you can get Parasound JC1+'s which is like comparing an old Jenny to an F22 Raptor.