In applying for a U.S. Government Job do I have to disclose that I plead no contest to a misdemeanor?

If it resulted in a conviction for a criminal offense you are going to have to reveal the conviction on the job application. If you've had nothing since then it is doubtful that this is going to cause you problems. However, if it is discovered that you lied on the job application and failed to reveal the conviction that is always grounds for discharge from your job. The fact that you plead no contest does not make a difference, since the result of a no contest plea still results in a conviction.