Wait until the forms are final. https://care-cdn.prodsupportsite.a.intuit.com/forms-availability/turbotax_nm_online_individual.html
This problem has been noted with several other state downloads.
You will need to contact TurboTax support for assistance with this issue.
Support is open from 5am to 5pm Pacific time, Monday thru Friday (Closed Christmas Day)
See this TurboTax support FAQ for contacting support - https://ttlc.intuit.com/turbotax-support/en-us/help-article/account-management/turbotax-phone-number/L0Od33nMQ_US_en_US?uid=lfgviwbm
Support can also be reached by messaging them on these pages https://www.facebook.com/turbotax/ and https://twitter.com/TeamTurboTax
The fix did not work for me- trying to download New Mexico for a business return
See if the fixes outlined in the TurboTax Help article State install/e-file update loop: State not installed after installation or TurboTax needs to update prior to e-file will remedy your state download issue.
That is the same fix as above and it did not fix it- frustrating