I disagree with your assumption that you need to be rich/making lots of money in order to save. It's not necesarily about being rich, it's also about spending less. People get very used to spending whatever it is they make. Lots of people live off $15k and manage to survive. Lots of people live of $100k and manage to wind up bankrupt. The trick is to not adjust your standard of living and expectations to be what you think you "deserve".

After getting a divorce a couple years ago, I got very used to living off of significantly less than the poverty line. After getting a "real" job, I've been making a concerted effort to not raise my standard of living TOO much. Despite making less than you (50% of my income would be below the poverty line), I still manage to only live off about half of what I make. Right now, the rest is going into paying off debts and student loans, but in about a year and a half those will be taken care of, and the rest can go into savings. (I may rebudget at that time and save less, if I feel like it would be a good idea to raise my standard of living again, then. However, I wouldn't have to.)