I had success today after having this problem. This was my situation. I had a domestic number listed in my tax return, I believe because it wouldn't let me input my international number (Moldova). Fortunately my wife ported her number before we departed the states and she can still get SMS messages to her gmail.
In my Intuit account I had my Moldova number listed, as that section allows you to enter international numbers. But this number wasn't verified like my email was. I believe the problem was Intuit wasn't transmitting the SMS to verify the number but it allowed you to leave the number there but unverified. I bet this is why the taxes wouldn't transmit though. Today I inserted my wife's US number and was able to get that verified. Then my taxes transmitted.
For those of you still having problems and don't have access to a US number to get your number verified, check to see if you have an unverified international number in your Intuit account, not on your tax return. It may still work if you just delete the unverified number as well, I didn't think to try that first but saw it gave me the option to delete my phone number.
I hope this helps a few people.
