You may wish to consider mailing in extensions to file your return until 10/15/18 and include any balances due with the extensions. On the extension, in the place for your wife's SSN, you can write in "Applied For." You should keep a copy of the extensions. Hopefully, by October your wife will have received her SSN.
Since your wife is not currently eligible to apply for a SSN, you can still apply for an ITIN with your return should you wish to file now.
