I guess you didn't see the Texas Instruments datasheet for the CD4081. With a 5V supply the typical shorted output current from the ordinary CD4081 is only 3mA and 4mA. Into an LED without a current-limiting resistor the current is even less.if you don't connect CMOS inputs they very likely float near the threshold that also keeps the output switches both open since their R.DS.ON-s at 5 V Vcc are apx. 300 ohm and (P-MOS) 50 ohm (N-MOS) they may pass 5 / 350 = 14 mA if you have 10 gates floating it's 140mA e.c. -- otherwise - if your pulse fronts and trails are sharp (the time that both switches are simultaneously open) - the CMOS consumes only few µA (micro ampers) . . .
Maybe you are thinking about a high speed Cmos gate (74HC series) that can supply much more output current.