If you didnt go to st. Grottlesex ( the network of private schools in new england) or andover. And then attend either yale or harvard undergrad. Or if you didn make it in the club that early, you would have at least went to eithe harvard law or yale law school. Dont even think about it. Volunteer first.
And to answer no, and hell no.
Frankly, getting into an Ivy League law school isn't that difficult. You need a good (some would say 3.75 or so is "great" but I think it's merely "good") GPA and a hot LSAT score. It is numbers-based and they oftentimes don't even look at your major (because your numbers reflect well on them regardless). Thus, you can strategize and get a great GPA in pottery or some other such inane bullshit, and it will carry the same muster as a degree from a STEM field. And, the LSAT can be studied for months in advance.
It's much harder to get into, e.g., business school or grad school.
Some numbers to back this up:
Harvard Kennedy School: 4.7%
Harvard Philosophy Program: 5%
Harvard Business School: 6.5%
Harvard Law School acceptance rate: 13%
Further, the HLS numbers are misleading because they get a large number of applications from losers who never had a chance but nonetheless give it a final shot (since law is for whatever reason prestigious a large number of people with no chance apply anyways, hoping for a miracle). This sort of thing isn't happening in, e.g., the philosophy department; there is going to be very little fluff in that pool of applications. So the actual acceptance rate among viable HLS applicants is higher than the official 13%.
In short, the first step to being a big politician requires only moderate intelligence and proper planning.