In-state price at a good state school is about $22k/year with room and board.
Figure you work a minimum wage 40 hours a week for 12 weeks during the summer. There's $3480. Now, figure you average 10 hours a week for the other 40 weeks of the year. There's $2900. Figure you're an outstanding student, so you got a one-time $2000 scholarship payout from winning a bunch of awards in high school.
There's a good chance at many large state schools that, even if you're focused, you'll need an extra semester or two due to limited course availability. Not counting the possibility of recovery from a leave of absence related to (mental) illness or family emergency, etc. Let's say you do one summer semester and it costs exactly half of a traditional year's net price.
So we're looking at:
+ $99k in bills and spending
- $10k for 3 summers of work
- $13k for 9 semesters of work
- $2k in total merit scholarship payout.
That leaves us with a $74k education. If mom and dad aren't buying, then there's $75k in principal. At 6.8% over 10 years (the federal government's deal, but it's capped; your actual rate from the private sector will be worse) that's $102k in payments.
That's for someone who did the "responsible" thing: went to state school, got scholarships, and worked continuously.
Now imagine that you go to a private school where the price after need-based financial aid is in the $30k-$40k range. Or, worse, that you go to private school and your parents are rich, so you qualify for no need-based financial aid at all, but your parents still don't want to fund your education. Then you're looking at $60k/year.
See where this is going? It's easier than you might think.