I have a W-2 from a Class Action settlement that missing the Employer State ID number for New Mexico and can not reach the settlement group. How to input a number?

If they did not withhold any state tax (no number in Box 17), delete the state abbreviation in Box 15 and leave the fields for 15-20 blank.  If there is a number in Box 17 you'll either need to continue to attempt to obtain that number or file your return by mail. 

Employer in not reachable and I need to file electronically. Is there another way to input a number?

Is there a state withholding amount in Box 17?

Yes

You can use the Federal ID Number if there is no State ID number on your W-2 and there is State Tax withheld.

Here's more info on State ID Numbers.