Its the driving device that might have the problem. ICs have a parameter called " fan out", for the TTL series, the outputs can deliver 10 mA, but each input needs 1 mA, so you can connect one output to ten inputs. Connecting 20 inputs to one output will not work. With the 4000 series chips its different as the inputs consume micro amps, but the outputs can still deliver 10 milliamps, so the fan out is enormous, certainly beyond what any one would need. But as Betwixt said each additional input has a small capacitance associated with it, so every extra input will delay the signal slightly.
Frank