If the IRS says the return still needs to be accepted after 24 hours and turbotax says that it has been accepted, does that mean IRS has received it? It has been 1 month.

[DonnaLO]

Does Where's My Refund?  say Pending, Processing, or do you actually see the words, "still needs to be accepted after 24 hours"?  You should have received 2 emails from TurboTax after you filed. 

The first would say something like:

You’re almost there

Be sure to keep an eye on your inbox to see if your return is accepted or rejected.

The second would say:

GREAT NEWS!!   <Your name>

Your Federal return was accepted by the IRS

You would have received 2 similar emails if you filed a state return also.   Keep those emails, those are your written proof that you filed and that your return was accepted.