You can't file jointly without either an SSN or an ITIN. Since you are expecting a SSN soon, you can file a request for automatic extension which will extend the deadline to October 18. You may be unable to e-file the extension request without an SSN either, but you can print the form and write "NRA" in the space for the SSN.
There are two other options. One is to file now as married filing separately, and file an amended return when you get the SSN to file jointly. But, amended returns take a long time to process, and there are some new rules that limit the tax benefits you can get if you amend to add an SSN that you did not have when you filed originally.
Or, you can file jointly now, and include a form W-7 application for an ITIN (international tax ID number). You would need a fake ITIN to get through the health insurance interview, then cover it with some white out and write "applied for" and print and mail your return along with the W-7. After you get the SSN, you would write a letter to the IRS telling them to cancel the ITIN and transfer your spouse's information to the new SSN.
All in all, your best option is to wait for the SSN.
