To be honest I think your chances of getting into T20s are fairly low. Your gpa and sat are low, your extra curriculars are alright, if you are aiming for a low T20 school then I would give you about a 10% chance (georgetown, etc), but I would give you a 0% chance in the Ivys. (Btw this is all comparative to other applicants for these universities, on a national scale your stats are great, just not for T20).
You didn’t include your demographics (sex, race, place of birth, socio-economic status), which could have a big impact. You’re also a junior, so try to retake the SAT/ACT and try and get an internship or something during the summer: that ought to help. Best of luck!
I think if you can get a higher SAT score it can greatly improve your chances. If you can get say a 1560 or higher then you may be able to get into low T20 schools.
Be aware that scores just need to meet a benchmark. There is no difference in admission chances between, say, 780 and 750. After you meet the benchmark your chances are all about other things. Also remember that admissions at tops schools is less about the individual and more about how you will contribute to the mix on campus.
GPAs in the 3.81-3.89 range are strange. They generally place a student in a very strong position in many really good colleges, but put them in a relatively weak position in a couple dozen very competitive colleges.
These GPA are in the top 1%-2% of all students applying to college, but, because of Common app, half of the students with GPAs above 3.9 are applying to the 20 most popular colleges. So at these popular colleges in most admitted students without hooks have GPAs above 3.90. However, students with GPAs above 3.8 are still being considered pretty seriously.
So the most popular colleges are likely very high reaches, but not out of reach. So Harvard would be a very high reach, while Georgetown would likely be a solid reach.
On the other hand, once you leave the most popular colleges, GPAs of over 3.80 are generally in the top 25% of applicants, so a colleges like George Washington University could be a safety or a low target.
Overall, it’s worth your while to apply at least to Georgetown, if you’re looking at a political science major.