The Harvard Government Department often receives 800+ applications a year, and similarly for other Harvard programs I'm involved in. As such, meeting with prospective students is, I regret, infeasible. [If we all did this, we wouldn't have time to teach the students already here, our students would leave, few would apply to attend, and we'd then have plenty of time to meet with you. But of course then you wouldn't want to come!] A better plan is to contact us after you're admitted.
In some Ph.D. programs (in the natural and physical sciences and in the social sciences in other countries), students are admitted to study with a specific individual faculty member who often makes the choice about admission; this is not the case in our program, where decisions are made by an admissions committee on behalf of the entire department. So you don't need to contact me to ask whether you can study with me; just apply to the department and if you get in you can.
You might be interested in this article I wrote about the admissions process in our department: "The Science of Political Science Graduate Admissions". The odds of being admitted are not high for anyone, but they do have to admit someone, and it might as well be you! I'm also happy to report, as a proud graduate of the University of Wisconsin, that there are many other great programs out there. Best of luck with the application process.