Accepted in TurboTax just means they have received your return but not processed it yet. This is normal; until they start processing it on their, you won't find record of it when tracking on their website. So if you contact the state or try look up your refund status, don't be surprised if they tell you "no record found."
Per New Mexico's Taxation & Revenue:
"The Department generally processes electronically filed returns claiming a refund within 6 to 8 weeks. A paper return received by the Department takes 8 to 12 weeks to process."
Once they have started processing your return, 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.
The accepted status in TurboTax will remain the same from here on out, since we no longer deal with the return once the state or IRS receives them.
