I'm a little confused on the original posters statement that the tech industry is saturated with H1 visa workers and americans can't find work. I'm a cisco engineer by training and also a heavy windows admin and do a little linux work on the side. I have NO COLLEGE DEGREE. I get a couple w2 job offers a week at 80k plus a year. I own a consulting firm and don't really want a "job". What I can say is an American with no accent and a personality will always out do a h1 looking for the same job even at 10k or 20k more a year. This is my opinion of the market in Phoenix it could be different in other parts of the country.
It depends upon the specialty, the hiring managers, the company, etc.
You won't be invited to work on a huge IT software project that will be mostly staffed by a H1B body shop. College degrees (good, bad, worthless or fake) are a prerequisite, often Masters Degree, because the H1Bs have those (for what they are worth), and it helps with their "can't find Americans" talking point. You don't get a chance at those jobs. Even if you have the degrees, you won't be seriously considered.
Here's an analogy. You can work as a handy-man or small independent contractor doing a variety of small construction type projects. You speak the language of your customers, word of mouth creates more work than you will ever be able to handle. Credentials, licenses and other bureaucratic nonsense don't matter to your customers.
On the other hand, for big construction projects, everyone is speaking Spanish. The people who do the actual hiring don't want to hire you, they hire family, friends, distant relatives, people from the same region as them. The executives don't want to hire you because you cost more and "make demands" of them. No jobs for you there.