But given it's a joke, it is much ado about nothing.
As I have already explained, that is incorrect.
To brush off something like this simply by framing it as a "joke" provides a far too easy avenue of escape, one that you seem all to eager to take.
It can be a joke, a bad joke, and also have import. I don't follow, nor do I agree, with your logic that because it is a joke, the consequences are immaterial and irrelevant, i.e., much ado about nothing.
This is a kid who said something stupid. On that we agree. Given that she is President of the College Republicans, and tweeted about how the idea of assassinating the US President is "tempting", it is a something more than "not a big deal". First, don't imply that assassinating the US President is "tempting", which means basically advocating to do it; second, as a leader, try to lead a little bit and not sound like all the crazies on tv.