Yes, most states are "at-will", which means you can be fired for any non-illegal reason at any time, barring any existing contracts.
For those abroad, remember that most of the time health insurance is tied to employment in the US... so when you get fired your costs also skyrocket (especially if you're the insurance source for your family).
Generally big tech companies don't give your manager the authority to blindly fire you, but only because that's a decision the company made.