She had two legitimate options: execute the President's instructions if she thought they are legal and moral, or resign if she thought they are illegal or immoral. She doesn't have the option to refuse to do her job.

Ministers and government officials resign all the time when they believe that their government's position is in error.

N.b.: I did not vote for Trump; I am not certain that everything in his immigration-related executive order is consistent with the law (but I am not certain that it's not, either: I am not a lawyer).