Set Field should work with your pop up menu. Can you describe what you did and how it failed?
Is the pop up setup as a 2 column value list with the first column of values hidden? It may be that you are entering the name from the second column instead of the value from the hidden column--which is what is actually stored in the field in this case.
You can set a variable to the contents of a container field.
I'm not sure what happened but its working fine now.
Thanks for your help.