It's very normal if your return still shows in pending status for an extended period of time after your federal return has been accepted. The processing times for each state can vary tremendously. "Pending" just means that your e-filed return is on its way and that the state hasn't accepted or rejected it yet. And until they accept or reject it, they won't have any record of it. Your state could possibly have a backlog, but only they can tell you that information. TurboTax has no way to access their systems to see if they do or not.
You can go here
How do I track my New Mexico tax refund? to get details to track your NM return. And most states have some type of note on their refund tracking page that states how long processing may take. If there is no note there, no need to be alarmed. You will get an email once the return has been accepted or rejected.
Per New Mexico's Taxation & Revenue:
Why is my state e-file still pending?