To confirm if you successfully e-filed your tax return you can check your e-file status to make sure it was transmitted. Please see the TurboTax FAQ How do I check my e-file status? for additional information.
Paper filed returns can take 6-8 weeks for processing. The IRS asks that you wait 4 weeks after the date you mailed your tax return before looking it up on the IRS Where's My Refund? site.
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When you efile you get back 2 emails. The first email only confirms the transmission. The second email says if the IRS (or state) Accepted or Rejected your efile.
When you log into your account you should also see the status and if it was Accepted or Rejected, Started, Printed, Ready to Mail, etc. what does it say?
If your account says Ready to Mail or Printed you need to actually print it out and mail it to the IRS and state yourself.