Get your taxes done using TurboTax

I do not know if they are eligible to apply for a social security number.  You will need to check with the immigration authorities.

If you check and they are not eligible to apply for a SSN, then you will need to apply for a Individual Taxpayer Identification Number (ITIN) for them.  You can only apply for an ITIN for them if they are not eligible for a SSN.

Here are some additional steps for filing married filing jointly if spouse needs an ITIN. 

• enter a dummy SSN for your wife and children NRA spouse's SSN blank and print a paper copy of your tax return- you can enter 999-88-9999 and other variations of this number for your children
  
• skip error check section if only error is for SSN
  
• under the file tab, you will need to select "file by mail" and print a copy of your federal income tax return.
• "white out" ALL the dummy SSNs and write next to the field for each SSN "Applied For"
  
• attach a statement, signed by both spouses, to your joint return for the first tax year for which the choice applies (Nonresident Spouse Treated as a Resident). It should contain the following information:
•  A declaration 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 that you choose to be treated as U.S. residents for the entire tax year.
• The name, address, and identification number of each spouse.
• apply for NRA spouse’s Individual Taxpayer Identification Number (ITIN) and children's ITINs using Form W-7 (Click ITIN).
  
• attach a copy of your Form W-7 (along with the necessary supporting documents) to your tax return (For the supporting documents, one option is for your NRA spouse to get a certified copy of his/her passport which will need to be included with your tax return filing.) Click here for IRS website  ITIN - Frequently Asked Questions .
• the best option is to take your completed tax return and original tax documents and completed W-7s to the IRS Taxpayer Assistance Center nearby.  Or you can mail your tax return along with your declaration statement, Form W-7 and supporting documents to the IRS. According to the IRS, 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, . Instead, send your return, Form W-7 and proof of identity and foreign status documents to:
  
       Internal Revenue Service
       Austin Service Center
       ITIN Operation
       P.O. Box 149342
       Austin, TX 78714-9342 
  
  You may also apply for an ITIN using the services of an IRS-authorized Acceptance Agent or visit some key IRS Taxpayer Assistance Center in lieu of mailing your information to the IRS in Austin.
• State filing - You will want to file an extension for your state until you receive your ITIN. This is because the application for your ITIN is a federal filing. Most state will not process your return without either a SSN or an ITIN. (However some states will accept state filings with W-7 attachments. Please contact your state for more information using the State Department of Revenue Contacts and ask if your state will accept a state tax return with a Form W-7 attached).  
  When the IRS assigns you an ITIN, update your returns (both federal and state) in TurboTax with this new information and then you should be able to e-file your state return.
  Because many states give an automatic extension when you file the federal extension Form 4868, just file a federal extension even if you don't think you will need it for your federal tax return.  But check with your state's Department of Revenue to make sure that your state doesn't have a separate state extension filing.