How do I efile the return I've already prepared when I have no employer state ID to enter into that field?

Several  states do not have a state income tax.  So these states will not show up in certain drop down lists.   Leave boxes 15, 16, and 17 blank when you enter a W-2 for these states.

Alaska, Florida, Nevada, South Dakota, Tennessee, Texas, Washington and Wyoming

Delete the TX from Box 15.   If all the boxes are blank in the state and local section (boxes 15-20) - you can e-file.   The message that says check your entries won't prevent e-file.   But you have to leave them all blank - so delete TX from box 15.