You are a worker in the USA, so you can get fired for anything, including calling in sick, or nothing, no reason at all. Your employer does not have to be fair. You just have to do your job and be grateful for it, or so says Glass Door, an employment guidance site.
Legally speaking, most employment contracts are at-will, meaning you can go and you can be let go for any reason or no reason. But employment is a relationship and you provide a service, so let us not live in fear. Try to be reasonable, and do your job, and you should not get fired for needing time unless your boss is a tyrant.