Do managers go around just firing people on the spot and the employees living in constant fear of getting canned?
Yes, and no.
Nearly all states are "at will" employment states, except for a few.
In an "at will" state, yes you can be fired for any reason, any time, unless you are under contract, or in a union.
But, there is more to it than that...
At a job too low paying to bother hassling with state government offices to get your job back or one that pays too little to justify court costs, yes, your firing will be pretty final. Besides, even if the job paid enough to justify going to court and getting your job back, things will probably be much worse at your workplace after the lawsuit. Lawyers will tell you that you do have a case, it just isn't a case that is worth pursuing.
But, it doesn't end there - the United States has unemployment insurance! Laying off employees or firing them without cause will leave them eligible for unemployment pay. Firings have to be legal (no EEOC, ADA, or discrimination,) and usually have to be "with cause". "With cause" needs to be a serious offense (like UPS's cardinal sins,) or there has to be three documented and verifiable reprimands (usually in writing) to give the employer cause.
Layoffs and firings without cause both qualify for unemployment pay. The employer would have to go to a hearing and prove they have cause, and the fired employee can appeal. Unemployment insurance claims cost the employer some, and make their unemployment insurance rate to go up especially if they are habitually firing without cause (like some brown companies.)