This is not uncommon at all; so there's no need to worry. Accepted in TurboTax just means the state has received your return. That is the status of your return; not your refund. But until they actually start reviewing and processing your return, their systems will have no record of it.  

Once they accept the return, they no longer provide any updates on your return or refund to TurboTax. The next step would be for them to process your return and approve your refund. Processing times vary from state to state. Some states have stated that they may take up to 90 days or longer to process returns and issue refunds.Patience is virtue when waiting on government to process returns.

Some states will post a notice on their Where's My Refund tracking page to let you know how long processing times will be; some do not. If your state has no notice, do not be alarmed. They will update the tracking page with a status once they have processed your return.