Slavery is illegal in the United States. Employment is termed "at will" in most states which means the employer can terminate an employee for any reason that does not violate the law AND employees can end employment freely as well.
Termination for reasons based on protected class is against the law. Those would include race, religion, national origin, ethnicity, gender, family status, disability and in some states, sexual orientation. States do differ. States can add to the protections but cannot offer protections less than those covered by Federal law. None-the-less, slavery IS illegal in the United States and in most countries.
No one, including a President, can be forced to perform any job. The president may have a contractual agreement (written, verbal or implied) to perform the duties of the job but that does not lift any laws against enslavement. Even with a contract, if there are circumstances preventing the President's performance of the contractual duties, those circumstances may be a way out of the consequences of non-performance. It really depends on the specific facts of the case. Who promised what, when, how, to whom and what was the consideration (payment/exchange) for performance and what occurrences have arisen that might reasonably prohibit performance?