I guess my comment could be an answer. You need to be able to click in the input field but you have assigned mouse clicks to some other event -- in this case printing. So another way to get something to happen when the mouse is "in" the input field is to use "MouseEntered"
EventHandler[InputField[Dynamic[s]], {"MouseEntered" :> (Print[1])}]
But whether this is appropriate would depend on what your actual problem is (I"m assuming this is a toy example).
Another alternative is to right click in the field:
EventHandler[InputField[Dynamic[s]], {{"MouseClicked", 2} :> (Print[1])}]
but for a left click within the input field @kguler's solution looks like it is what you need.
EventHandler[InputField[Dynamic[s]], {"MouseEntered" :> (Print[1])}]– Mike Honeychurch Dec 20 '12 at 5:37