Okay, if they want to they can fire you. You live in an "at will" state. They can fire at will, you can quit at will. End of story. They do not have to have proof, they do not have to have any good reason. You cannot sue them for firing you.
The recourse that you do have is that when you file for unemployment insurance after being fired, the company has to demonstrate that they had a good, valid misconduct reason for you to be fired, or you will be approved for benefits, and this will cost them money eventually.
If you are a regular employee, if the business has more than one or two employees (making them an unemployment covered employer), if you have enough covered wages in the past 18 months, then you would have enough wages to set up a claim for unemployment insurance.
This is your only protection from being fired arbitrarily from your job, the downside that they do have to pay in unemployment taxes and it will cause their taxes to go up if you are approved to draw from them.
Unemployment benefits aren't nearly as much money as you'd make working, and they are finite, they do end, and you are required to be searching for other jobs while you receive them. They're to get you by, tide you over until you find something else.
I strongly suggest that you begin looking for that "something else" right now, before they fire you or start cutting your hours. But do not quit this job because you think they're about to fire you. This will not help your references or cause it to be easier to get another job like you believe it will. If they start cutting your hours, to force you to quit (making it much harder for you to get unemployment benefits) you have two possible recourses.
If they walk in and say, "Okay, starting this week, we're cutting your hours from 40 to 8, you will no longer have health care or benefits provided," it is probably better for you to say, "Okay, then if this is how it is, I quit." And then you immediately file for unemployment benefits. Doing that is called "forcing a quit." It's pretty much the same as firing someone.
But if they start chopping your hours a few here and a few there, less and less,keep up with what you are making in gross pay, and when it becomes less than you could draw in a week of unemployment, file for partial benefits. This means you keep working, but you are making less than you could receive in a week of unemployment insurance, so you can use unemployment insurance to supplement your wages. This will usually force the employer to either put you back to work full time or fire you outright.
Once the bloom is off the rose, so to speak with this employer, the old "we may fire you and we may not" deal, it would be a real good idea to assume this job will be done soon and begin making a vigorous job search for something else. Even if you were innocent as a baby's breath, they've accused, and they'll suspect and will treat you as if you were at fault. They can legally do this, regardless of how much or how little proof they have, but you always have that option to move on.
