Personally I feel that Soacial Security is a sham and I don’t think I will ever see a single dollar that I pay into it. I feel that that I can invest 15% of my paycheck much better than the government can. Recently I read this article,
http://www.pensionreform.org/articles/farago.html , and was wondering if this is a real possiblity.
The answer to the OP is mostly a No with a qualified Yes.
YOU cannot opt out of your own accord. At least not if you expect to stay out of jail. Your employer automatically withdraws those funds from your paycheck and if you’re self-employed and don’t pay in I imagine you’d be hearing from the IRS pretty fast.
The article you linked to basically said that not even the state of Oregon could opt its citizens out on its own. The resolution was merely to direct Oregon’s congressional members to draft a bill that would allow states to opt-out if the STATE chooses (again…not up to individuals).
While I agree with the OP about wondering if there’ll be any money there when I retire you have to be VERY careful when twiddling with SS. If such a bill was passed that allowed states to back away from SS the system could easily collapse (as it is projected to do anyway in 20 or so years). While you may consider that a good thing there are a lot of people who rely on SS as their only income. I know SS was intended to be supplemental income only and not the only money you live on but a great many people do so nevertheless. If SS collapsed tomorrow you’d have thousands of senior citizens on the street.
Sure, you can opt out. The solutions for doing so aren’t all that attractive though. One, you could quit working and two you could move out of the country.
You could have a powerful union like the teachers do. I’m pretty sure they don’t have to participate in SS. They have their own plan, at least my wife did when she worked at a school in Texas.
Teachers may have their own retirement system depending on the state, as may government workers at different levels. Anyone who works for the State of Ohio (including teachers) is exempted from Social Security; the money instead goes into the State Employees Retirement System.
I believe the military is also exempted from SS, but I’d check on that more fully before joining up 
LL
“I’ve been working on the railroad…”
My father didn’t participate in SS. Instead, he participated in the Railroad Retirement System.
You could also move to Pennsylvania and join the Amish. They don’t pay into SS, because they don’t collect on it when they are retired. They are exempt on religious grounds.
But then I’d have to give up the Straight Dope 
Nope, I’m afraid not, at least not these days. My father is a federal employee and he pays social security as well, although I have no idea if all gov’t employees have to pay.