The inputs are usually much more sensitive than microamps - the datasheets say something like a microamp, but that's playing safe across the whole temperature range (at high temperatures the protection diodes start to leak a bit). You can assume the (DC) input current is zero to a very good approximation - the gates of the input FETs are insulated with silicon dioxide, which is basically the same material as glass. The voltage is sensed by the electric field it generates across this (incredibly thin) oxide layer, so there is no actual need for any current to flow in the steady state.
In practice the varying electric fields around the pin and its PCB trace will affect the input voltage strongly when it is unconnected (floating) like this - bring a finger close will often give a strong 50 or 60Hz signal from the omnipresent mains voltages in your building. This can be a useful test for a floating input - the input protection diodes clip the induced voltage and prevent the input transistor gate oxide from being damaged (but beware static electricity on dry winter days which can overload this protection).