To me that X is the amount needed to just survive, maybe a little more. Right now I'm working far more that I'd like, that is, making far more money than I need, since I'm far from being a big spender but I love having time for studying or for long walks at the beach (my most expensive vice is in fact studying, which is far cheaper in my country than in the US). It sucks that in practice there's no way to work less than 40 hours a week, and less than 11 months a year, save for being unemployed (for quite a few reasons, becoming a freelance would not improve that for me).
Right now, with my savings, I could expend 2 or 3 years without working, but there is an implicit blackmail (companies don't hire you if you have been unemployed for too long) that prevents me from taking a long sabbatical.
However, like you, I still recognize that I'm lucky. Some people don't have the option of having even a month without a job.