My dad worked 14+ hour days during the summer at union construction jobs after high school. This was the late 1950s to early 1960s, four years straight. He lived at home during this time, so had room & board covered. He made enough money every summer that he was able to pay the full cost of a private college education, afford to maintain and drive an automobile, and have spending money for various & sundry other life expenses.
Fast forward 30 years and I followed his example, with similar circumstances (room & board covered), but there were no union jobs. My summer earnings covered roughly half the cost of schooling at a state university at in-state residence rates and nothing else.
The years between had seen construction/labor wages not just stagnate, but lose value while the cost of a college education increased at several times the rate of inflation. My folks were very helpful and my dad provided me more assistance than his folks had when he was in school. He realized that a business degree you could get with relatively little effort was no longer worth much and that you had to go STEM or go home for a bachelors to be worth much. And most STEM courses of study require a level of commitment that working full time during school terms while taking a full course load is not tenable even for the brightest. [For example, one single credit of physics lab required ~30 hours per week to make a passing grade. Very much a "learn by doing for yourself" atmosphere at that dept.] Looking at mean wages for construction jobs and state school costs, my experience was easier than someone following the same path today vs the 1990s.
So, no, it is not impossible to work your way through college. But it has gotten much harder to do as time passed. Not only has the dollar-cost of a college education dramatically increased, but so has the opportunity cost when a student must string out his education by an extra year or four as a part-time student. Instead of a 22YO graduate, we see more 26YO graduates who went straight from HS to college. Generally with more debt.
