How long until after I file does the status change from pending?

It is not unusual for your return to stay in pending status for several days sometimes longer depending on the back log of returns filed and time it takes for the IRS to process them. Keep checking the IRS Where’s My Refund? site for updates. The tool is updated daily (usually in the overnight hours) so you don’t need to check more often. Please see the TurboTax FAQ What does "Pending" mean? for additional information. 

Millions of e-files have been backlogged on servers for weeks.  This week the IRS began to accept/reject e-files.  When yours makes it through that pipeline, you will get an email.

When you e-file your federal return you will receive two emails from TurboTax.  The first one will say that your return was submitted.  The second email will tell you if your federal return was accepted or rejected.  If you e-filed a state return, there will be a third email to tell you if the state accepted or rejected your state return.