Yes. YOU, as the parent and the person who is paying and the person who has probably 30 years of experience as a legal adult who makes money decisions and can make a legal contract (as opposed to your child, who might not even be 18 years old yet), should CALL the admissions office, ask for a call back from the person who can help you with appealing a merit offer, and then explain to them very nicely that while your child is thrilled with the idea of attending GW, the price difference is too much for your means, and would it be possible for them to up their offer, to match the cost of attendance at UConn? You never know what you can get by asking nicely. This is not an admissions decision; your child is already accepted. You run the money, unless you sincerely believe that your child has better maturity and negotiating skills than you do.
BTW, if your child’s goal is political science, UConn is not that far from Hartford, the state capitol of CT, so if what they’re interested in is politics, governance, etc, they could still get experience with an internship or a job in politics/governance in Hartford (to which there’s public transportation from Storrs), and that skill would be transferable to the national arena. They could also get a job in DC right after college, and go to law school in DC, and intern in DC while attending law school.