You should file an extension since you are expecting another tax form. This extends your filing deadline to October 15. Since it's an extension of time to file your paperwork and not an extension of time to pay any taxes you owe, you'll need to send payment (either by check or direct debit) along with it. You should have some idea of how much income will be reported on the K-1, so be sure to include it when figuring out how much money to send to the IRS (assuming you have a balance due and not a refund). You don't want to underestimate this payment because the IRS will charge interest on the difference until it is paid.
It's easy to file an extension with TurboTax. Click here to get started.