A plea bargain can be extended at any time. If it is a crime with a victim who is protected by the Victim Bill of Rights, the DA can't offer you a plea bargain until contacting the victim first, which does not usually happen. Never enter a plea of guilty or no contest to the charges as charged. Always ask to speak with the DA about a plea bargain and ask for additional time to consult with an attorney. No judge will hold that against you and the judge would actually prefer for you to make an informed decision instead of just shooting from the hip.
The information provided in this answer does not create an attorney-client relationship and is not considered to be legal advice.
Mr. Leroi is correct. Plea disposition offers usually start at the time of your first court appearance, whether it be for an advisement or an arraignment. A criminal defense attorney will maximize the chances of you receiving a better offer!
In no way am I offering you legal advice, and in no way has my comment created an attorney-client relationship. You are not to rely upon my note above in any way, but insted need to sit down with counsel and share all relevant facts before receiving fully-informed legal advice. If you want to be completely sure of your rights, you must sit down with an experienced criminal defense attorney to be fully aware of your rights.
At the first appearance ask the court to set the case for a pretrial conference with the DAs Office. At the pretrial, make no admissions, just try to tell the DA what kind of person you are and the absence of any wrongdoing in your past. (Assumed by me because of your question).
You are best advised to get an attorney. He can get discovery, analyze the case and deal at a more even level with the DA, maximizing you chances for a good plea bargain offer.