You can still file an extension and if you think you will some amount, pay that or pay nothing if you really don't know. What will happen is that you will not be charged any late filing fees for not filing by tonight's deadline, and any amount that you end up owing for 2015 will be assessed interest and fees for late payment. If you pay something tonight and end up getting a refund, the amount you pay now will be considered as payment and your refund will be calculated with that in mind.
You can still file an extension and if you think you will some amount, pay that or pay nothing if you really don't know. What will happen is that you will not be charged any late filing fees for not filing by tonight's deadline, and any amount that you end up owing for 2015 will be assessed interest and fees for late payment. If you pay something tonight and end up getting a refund, the amount you pay now will be considered as payment and your refund will be calculated with that in mind.
I tried filing through the turbo tax website but it says "Let's estimate the amount you owe." I can't go any further without putting an amount in. Still confused.
Try to estimate how much you think you will owe and put that amount. If you don't think you will owe anything, put 0. If the IRS thinks you owe more than that, they will calculate that after you file your return for the year, which will be due Oct. 15th if you file the extension.
If I just make my best guess, can I do that without getting into trouble?
The IRS will eventually calculate how much you owe based upon what is sent to them and when you file your return, any difference in what you owe and what is paid now will be charged interest and if you are due a refund, your payment now will be applied against that amount owed.