Have you already achieved your 2300, A's and B's in AP classes, and gotten leadership positions? While that question is not meant to deter you, it does beg to differ whether or not these things are actualities, not eventualities.
Okay, onto the actual answer...
C's are not the end of the world, but neither are they very good. All the top schools, Yale and Columbia included, receive applicants from all over the country, with very diverse profiles and applications. Two C's will not make or break you, but they will not help your chances. In looking at GPA, if your overall GPA is still high, those C's will not affect you as much.
However, grades, SAT scores, and leadership positions are only a portion of the college application process. Do you do extracurricular activities? If not... well, start! I recommend volunteering, since I personally get a kick out of doing it, and it looks great. Win-win scenario. If you are EC'ing away, make sure to do things you love, not just things that you think will look good on an application. While all applicants are guilty of some 'stacking', colleges will ultimately love it more if you show what you love over if you show what you tried to do. Sports, arts, anything--prove to colleges that you enjoy your activities and you will be that much better off for it.
Nonetheless, it is difficult for anybody to guarantee admission at a top-rated school. So many qualified, highly competitive people apply to Harvard, Yale, etc., that it is difficult for application officers to pick them out of a crowd. Even tailored-for-college students do not always get in, so it is still a wild chance. However, you can increase your chances with your (and my) aforementioned activities, as well as write good essays.
One last thing, about the essay. Statistically, 95% of essays don't help or harm the applicant, 2% harm, and 3% improve one's chances. While the number is low (3%), this is not to say that you shouldn't try to write good essays. If you can be in the 3%, this will help you beat out 97% of people when essays are being considered, right off the bat. This may turn the tide when committees are choosing between two candidates with similar credentials.
As a wrap-up, don't worry too much about the C's. Do well these next two (or one?) year, do your extracurriculars, and prepare well for essays. Just... don't forget to live life.
Good luck on your application, and I hope you get into the schools you want to get into.