Finally, it was suggested that I control the power of some ICs by hooking
up their power lines to a small FET.  The Shift registers are the biggest
offender as far as power goes (everything else goes to sleep).  However,
they will be required to be able to provide ~45mA for the LEDs each
(worst-case).  Any recommendations as to a FET suitable for this app?
(small package, fairly high current, low voltage).



Texas Instruments makes some parts designed for this type of application,
like the TPS2010, or maybe the TPS1100 family might work.