If they don't, Nathan will decide on the Securities and Exchange Commission's motion to find Musk in contempt.
As part of the settlement, before he tweets, Musk agreed to seek approval from a business attorney.
The judge was not impressed, however, and told both sides to "Take a deep breath, put your reasonableness trousers on, and work this out", giving them until this Thursday to settle their differences out of court.
The SEC wants Nathan to fine Musk for allegedly violating a court-approved settlement requiring his tweets to be approved by a lawyer if they disclose important company facts.
The judge also wrote that if Musk is located in contempt, briefs will be written by both sides.
Musk had until Monday to explain why he shouldn't be held him in contempt of court over a tweet on February 19, published outside trading hours, which the SEC said violated a September settlement agreement with the unpredictable CEO. Musk said his tweet did not need pre-approval because it was. The portfolio manager for Tesla's largest shareholder after Musk said the CEO may better serve the company by being less outspoken.
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Tesla is also upgrading the FSD computer in all of its cars soon, and will even retrofit cars that have FSD with the new computer should the owner requests it. Electrek notes, however, that it's unclear if all cars are getting the new computer or not. His attorneys said the SEC was violating his First Amendment rights to free speech.
In a statement following the hearing, Musk indicated he's ready to work a bargain.
The problem within the tweets of Musk stems from a settlement reached previous year following Musk tweeted that he had secured the funds to take Tesla personal at $420 an share - a premium over the price at that time - he didn't. Last August, that conversation, delivered the stock of the company on a ride.
Musk later backed off the idea of taking the company private, but regulators concluded he had not lined up the money to pull off the deal.
The tweet that prompted the SEC move said that Tesla will manufacture half a million cars this year.