The October 31st date is the time you have to sign into your Online account to file your return, that means you can prepare your return until October 31st & print and mail it in. The Online version shuts down after October 31st.
If your original return is rejected, you have until October 20th to re-e-file, after that date you need to mail in your return.
That is why in that link it has the following:
Missed the October 31 deadline? Find out how to finish and file your return in the TurboTax CD/download software.
