US employment law is the mirror image of much of Europe, built around at-will employment — and heavily layered with state variation.
At-will employment
In nearly every state, employment is at-will: either side can end it at any time, for any reason or no reason, without notice or severance. (Montana is the notable exception.)
The exceptions that matter
At-will is bounded by important limits: you cannot dismiss for an unlawful reason — federal statutes like Title VII, the ADA and the ADEA prohibit discrimination and retaliation — and exceptions exist for public policy and implied contract.
Mass layoffs and severance
The federal WARN Act requires advance notice of large layoffs or plant closings. There is generally no statutory severance; any severance is contractual.
State variation
States diverge widely — California, for example, is far more protective on wages, leave and non-competes — so the state is decisive.
For foreign employers
"At-will" does not mean "no risk". A verified US colleague in the relevant state can keep a termination defensible.
State and federal rules change — confirm with admitted US counsel in that state.