One the best accidents in my life was getting a student job. Without the 'years of experience' it gave me, I don't think employers would have given me the time of day. With it, I did get the time of day and most places cared more about the work I'd been doing than the grades I'd been getting.
"Entry-level" job descriptions that require 2-4 years experience don't actually require 2-4 years experience. They require no experience but the gumption and savvy to recognize that what the employer's actually testing for is your ability to read between the lines in what they ask, learn what they value, develop skills quickly, and market yourself well enough to convince him you have those skills.
Pretty much everyone in the field knows that you can train an enthusiastic and reasonably intelligent newbie up to a useful junior dev in about 2 months. What they don't know is whether you're an enthusiastic and reasonably intelligent newbie. The skills I mention above - reading your boss's mind, learning things you don't know, and convincing people to take a chance - are far more important than any technical skills you can learn.