I installed a new gfci outlet on the exterior of my house. I picked up the hot line and the neutral from an indoor switch box that has one switch for the outdoor light and a 3 way switch for the basement lights.

To begin with, switches do not use Neutral, they are for hot wires only.

With the advent of the 2011 NEC, a Neutral is required to be present in a switch box for speciality switches that might require a Neutral conductor.

The presence of a White or Gray conductor connected to a switch is fairly normal. However, there should be a permanent marking on this wire to signify that it is being used as a hot conductor to carry power to a switch, only.

So I question how you got "Neutral" to your GFCI receptacle.

Donf, I believe he says hot and neutral come from switch______box, not switch.
Widgekit, remove anything on the load side first and test, Anything on the load side has to be equally taken off the load side, You can't use a hot from the load side and a neutral from another circuit, if hot and neutral do not have the same load, it will trip.