Employer: "We need to search your car."
Employee: OK, but you need to get a warrant and do it legally.
Only if your employer is the government.
It is "at will employment" not "right to work."
"Right to work" deals with required union membership.
At will employment is used in most states, but a contracts can still exist, and some states have 'public policy' exceptions (you cannot fire an employee for certain specific things that are 'public policy').
Unless their is a state law protecting you, your employer does not need a warrant to search your car that is on his property.
In an 'at will' state absent a contract you can be fired for almost ANY reason (the employer must not discriminate against 'protected groups' though).
Failing to allow a search that you most likely put on notice about in the employee handbook is grounds for termination;
Insubordination is ground for termination.
You can also quit at any time without notice (though you may have a hard time getting a decent reference) if you do not have an employment contract and are 'at will.'