You cannot file Form 2553 using TurboTax if you E-FIle your return. Form 2553 is available to print in TurboTax Business; however, you will have to print and mail the form. For instructions on how and where to file Form 2553, see the IRS Instructions for Form 2553
Even though your Form 2553 will be late, you can still file Form 1120-s. You will have to request relief for a late election, but it shouldn't be a problem. Just explain that you were unaware of the filing deadline requirement. You can print and mail your entire return and include Form 2553, or you can e-file your return and mail form 2553 separately.