When you say that you've "done" the problems in the OG, what do you mean? There is little value in just doing problems. You should be analyzing every problem to find the best way to solve it, to see why the wrong answers are wrong, and to find some sort of "takeaway" or rule for every problem that can be applied to future problems. Just for comparison, when I studied for the GMAT I probably spent an average of 5 minutes working every problem. Some were quick, of course, and some took 20 minutes or more. It took me about 6 weeks to "do" the OG.
As for improving: yes, you can certainly improve in 12 days. The 780, however, may be a bit of a stretch. Remember that 780 is well above 99th percentile. Something like 1 out of 2,000 test takers will get a score that high. Many Veritas instructors, myself included, who have been teaching and studying the GMAT for years still haven't hit 780. You should definitely set your goals high, but don't be shocked when the score is something under 780!
Overconfidence tends to come from not seeing the "issue" in problems, so you feel like you knew what you were doing but got the problem wrong, anyway. The more practice problems you do (and by "do" I mean "analyze", as described above), the more of these issues you will see. In my experience, the better I get at the GMAT, the longer I take to do the test.
Jim S. | GMAT Instructor | Veritas Prep