The short answer is no. Especially if you can get into a quality state university, and UW Madison is one of those.
Four years at Madison, without any financial aid, is currently about $110K in state. Four years at Georgetown or similar is $300K+, and likely $325K by the time your graduate. Think what you could do with the extra $200K. Go to an elite law school, for example. Or if you decide not to go to law school after graduation (and that happens, as it did with me), maybe you get an MBA (again, like I did), or you go right into the workforce, $200K richer.
If you decide to go to law school, being in Madison, you will have access to politics at the state level at the Capitol, and may have less competition getting an internship than you would in DC. Also, my best friend from high school was married to a top patent attorney making half a million a year at a large firm. She went undergrad to a regional state school, not even top ranked. Her law school was Top 20, but she became well sought after based on the fact she had her engineering and law degrees at first, and then her work experience, not her schoolâs ranking.
I suggest you read the book by Frank Bruni, âWhere you go is not who you will beâ, which makes a strong case for not defining yourself by your diploma. Lots of people go to less well know, lower ranked schools and do very well. The Atlantic in 2014 published an article on which factors are most important in hiring on recent grads. Look at where college reputation is located (hint: the very bottom). Your internships and employment during college are more important. https://www.theatlantic.com/business/archive/2014/08/the-thing-employers-look-for-when-hiring-recent-graduates/378693/
I will leave you with this. Last week, my friends and I, all of us University of Michigan grads, a Top 5 public university, got together. We discussed if it matters where you go to school for undergrad. All three agreed it doesnât, especially with the high cost. Save your money for grad school. If you want to splurge then, thatâs a better investment.