Can I request an extension to file my taxes through turbotax? I'm waiting on a document from being on short term disability last year..

Yes.  Click here to file an extension.  Remember an extension is just for extra time to file, not extra time to pay.  If you are going to owe anything, you will still need to pay by April 15th. 

You can pay directly via the IRS website which is the recommended way or you can pay by check.  Be sure to include your SSN on your check and the tax year. 

to request an extension on IRS.gov you must pay some non-zero amount.

you must have your bank info

you must have filed previously.

You can still put a signed form 4868 in the Post Office mailbox without money until midnight

properly stamped and addressed, of course.