Get your taxes done using TurboTax

The actual IRS instructions for form 1040 state:

If your spouse doesn’t have and isn’t required to have an SSN or ITIN, enter “NRA” in the entry space below the filing status checkboxes. For electronic filing, enter the spouse's name or “NRA” if the spouse doesn’t have an SSN or ITIN in the entry space below the filing status check-boxes.

That does not mean that the spouse's name or SSN should be "NRA" it refers to different box on the form 1040.  See picture.

I don't know whether Turbotax supports e-filing without the SSN or ITIN.  Just because the IRS allows it, doesn't guarantee that Turbotax is programmed to allow it.  (Some of the rules for the e-file system are mandatory and some are optional, apparently.  Turbotax also doesn't allow PDF attachments even though the IRS permits it and some other tax software allows it.)

What you should be looking for is not the ability to write "NRA" in the box for the SSN (which is probably programmed to only accept numerals).  What you would be looking for (based on how Turbotax handles similar issues) is a checkbox on your spouse's information page, where there are several other checkboxes for other special circumstances.  

Frankly, I would not hold out hope that if you called support, you would get a correct answer, since this a a fairly technical area and the support operators are many layers separated from the programmers.  If Turbotax won't allow you to e-file, I suspect you will have to file by mail or find a different software provider.