Not a lawyer but broadly most forms of employment in the US is considered to be 'at will' and can be terminated by either party at any time for most any reason (excluding membership of a protected class). If you were fired for failing to respond to the yes-or-resign I believe you would be able to claim unemployment because they can't force you to resign and changing the terms of employment to force a resignation is a 'constructive dismissal'. American employers tend to be big fans of lying and hoping you don't know your rights though, or denying valid unemployment claims because they know not everyone will contest it.
Some people do have employment contracts with more consideration but as I understand it that mostly applies to union work and C suite executive positions.