Request for my wife's Taxpayer Identification Number

Yes, you can prepare the return using TurboTax but you will have to file it by mail. 

You can file a joint 2017 U.S. tax return with your non-resident spouse and that spouse can be treated as a U.S. resident for U.S. Federal Individual Income Tax purposes. 

Steps:

• Your non-resident spouse will have to obtain an Individual Taxpayer Identification Number (ITIN) using Form W-7, 
• You will have to file your return by mail (along with the Form W-7)
• You will have to include a statement, signed by both of you, declaring that one spouse was a non-resident alien and the other spouse a U.S. citizen or resident alien on the last day of your tax year, and the non-resident spouse  chooses to be treated as U.S. resident for the entire tax year.

How do I apply for an ITIN? Use the latest revision of Form W-7, Application for IRS Individual Taxpayer Identification Number to apply. Attach a valid federal income tax return, unless you qualify for an exception, and include your original proof of identity or copies certified by issuing agency and foreign status documents.

See Instructions for Form W-7

Because you are filing your tax return as an attachment to your ITIN application, you should not mail your return to the address listed in the Form 1040, 1040A or 1040EZ instructions. Instead, mail your return, Form W-7 and proof of identity and foreign status documents to:

Internal Revenue Service ITIN Operation

P.O. Box 149342

Austin, TX 78714-9342 

For additional information, see the IRS web article Nonresident Spouse Treated as a Resident

Important: You can't prepare and print a tax return in TurboTax without an ITIN or SSN for you, your spouse and any dependents.

The work-around for this situation is to use "Dummy" SSN/ITINs for your dependents. to prepare the return. You can use your own SSN/ITIN with different last numbers. 

Or use "305-44-0001, 0002, 0003 etc.", a dummy number we use for training.

This should allow you to get through the Smart Checks and Reviews and print your return for filing by mail. "Erase" or white-out the dummy SSN/ITINs and replace with "Applied For".