Once your return has been transmitted to the IRS and your state department of revenue and they accept it, TurboTax has no way of finding any information regarding your return. IRS representatives will be the only ones that are able to research the status of your federal return. You can call them at 1-800-829-1040, but prepare for potentially long wait times.
The following TurboTax FAQ explains possible reasons why your return may be taking longer to get approved.
You would need to contact your state department of revenue to find out any information on your state return. The following TurboTax FAQ explains how to do so.