So, I’m slated to fail my AP Government class with at least a D, but I’m confident I can score highly on the AP exam for it. I’m wondering if colleges would excuse the bad grade because I scored highly on the Exam, specifically NYU. Thanks.
No. It will look better than getting a low grade in the class and a low exam score, but lots of people do well on both.
My HS had a policy that if you got a 5 on the AP, you automatically got an A in the class (obviously you had mastered the material). It might be worth proposing to the administration. I know it saved my behind from failing economics (it was first hour and I am a night owl).
The score you get on the AP exam usually matters more if you are expecting college credit for the course. At my daughter’s college an AP exam score of 4 or 5 got college credit for an equivalent course. I don’t think that the course grade had any impact.
I don’t think either madequate much difference from an admissions perspective.
Well given my aversion to waking up before 10:30am, I would have failed economics (voted most likely not to show up for graduation). And the ding to my GPA might have hurt me a little somewhere down the road. 
It’s really hard to predict what admissions committees will think of you. Just do the best you can.