You can enter the W-2s with the correct Social Security number (yours) and go ahead and file. This could cause a problem (depending on how long it takes to get the W-2Cs) as the information on your return won't agree with what the IRS has on file for you. Another option, and perhaps a better one would be to file an extension and wait until you receive the corrected W-s. If you do the later, you and have tax due, you should pay your tax with your extension. See the following FAQ on how to file an extension with TurboTax:
https://ttlc.intuit.com/replies/3301811
