Filing an extension does not actually give you an extension of time to pay your taxes due (and there is no such extension). If you don't pay in full by April 18th, then you will be charged certain interest and penalties. But, filing an extension does help alleviate some of them.
There are three types of interest and penalties: interest, failure to pay penalty, and failure to file penalty. The failure to file penalty is by FAR the most punitive and that penalty will NOT be applied if you timely file an extension. The balance due will still accumulate interest and the failure to pay penalty so you should pay as much as you can by April 18th.
If you are otherwise ready to file your return, then you should go ahead and file your return and apply for an installment agreement -
You can apply for an agreement online directly with the IRS. I actually recommend you follow this route because the fees the IRS charges to set up an agreement are less with this method and you get an immediate response on your application. You can file your return as normal through TurboTax and then instead of making a payment, you will tell the program you are going to pay by check and then ignore the voucher that prints out (or you can make a partial payment with it). Then, go to the link below and file for an installment agreement with the IRS.