Tax Expert DawnC has a workaround here:

There seems to be an issue with e-filing when there is not a US phone number listed in your Intuit Online account.   When you are signed into your account, click on Intuit Account in the bottom left corner.    The error is not from the phone number on your tax return but rather the phone number attached to your Intuit (TurboTax) account.  

Change your phone number to a US number in the Intuit Account of TurboTax.   No need to verify this number in the Intuit Account just click exit when you are done. Then go back to your return and continue filing.   Don't use a Google Voice number, a Skype number, or any other non-US or non-verifiable phone number.  Again, you don't have to verify the number but the number needs to be verifiable.  

You may be able to leave the phone number field blank on your Intuit account and e-file your return.  No matter which option you use, make sure to update your account with your correct phone number once your return is e-filed.  

View solution in original post

This totally worked for me. I changed the Intuit number (not the number on the tax return) to a USA number that could get SMS and it worked like a charm! Many thanks!