I had this same problem.
First thing to know is that the payment window may pop up as an additional window in turbo tax or may pop up in a different browser window; i.e. internet explorer (be sure to check all the icons at the bottom of you task bar).
Second, close and restart turbo tax program. It will save your progress thus far. When you reopen the program it will perform updates. This is ultimately what fixed the problem for me. ( Again, it opens in a separate browser window, not directly within the turbo tax program.)
