It's worse than that - when I enter $10 paid my federal tax due goes down by $10. When I up it to $20, it goes down another $10. If I enter $81 the amount of federal tax due shown is $81 than it was before. But if I enter $82 it jumps up by a few hundred dollars. There's a bug in the program.
It sounds like at $82 you likely trigger Alternative Minimum Tax (AMT) which then completely jumbles up your entire tax return.
After you see the tax increase as you add more tax paid take a look at the forms in your return (under tax tools if you're online or just switch to forms if you're not) and if you see form 6251 listed, this is probably what is going on.
There are a lot of interdependences that don't make sense when you're watching that refund meter. Don't assume the software is wrong but take a good look at the full return before you transmit it.