This is a known mistake with Manipulateand Slider, especially if there are more 2^31discrete "steps" for the slider .
As a workaround, you can do the following, for example:
Manipulate[Round[k], {k, 0, 10^100}]
Without specifying the step size (fourth argument), you allow the slider to set non-integer values for the variable, but you can work around this using Round(or IntegerPart).
Hope this helps!