Legal Question in Constitutional Law in California

Yes. There are a variety of reasons why it would be impractical for the First Lady to have a regular job, but the law would allow it.

The president's spouse is not a government official or employee. Michelle Obama resigned her $350,000 per year position as a Chicago hospital executive when her husband was elected president. If she were to accept private employment, this might be a conflict of interest for the president; and she is still a licensed attorney who is subject to ethical rules regarding conflicts of interest. She has ceremonial duties as First Lady which might include service as a director or trustee of various artistic and/or charitable organizations. Whether or not she is allowed to, or does, accept remuneration for these positions, or whether she gives the money to charity, I have no idea. Like many famous people, she is in demand as a lecturer, and she could possibly charge a six-figure honorarium for personal appearances (just as does former governor Sarah Palin).. Depending on who is paying and what becomes of any money over and above her travel expenses, any such arrangement could also pose a conflict of interest for the president. Her primary job is to get her husband re-elected, and that includes not doing anything that might raise the appearance of a conflict of interest or other impropriety.