Originally Published: 19 JUL 22 07:58 ET

Updated: 19 JUL 22 08:54 ET

By Clare Duffy, CNN Business

(CNN) -- Lawyers for Twitter and Elon Musk will have their first chance to square off in court on Tuesday in the case over whether the billionaire Tesla CEO should be forced to follow through with his $44 billion deal to buy the social media company.

At issue in Tuesday's hearing is how soon the case will go to trial. When it filed the suit last week, days after Musk moved to terminate the deal, Twitter also filed a motion to expedite the proceedings and requested a four-day trial in September. Musk's legal team is opposing the motion.

Even with this scheduling dispute, the stakes are high for Twitter. The company was already struggling to grow its user base and advertising business before Musk's involvement, and now it and many other tech companies are pulling back on costs amid rampant inflation and fears of a recession. Twitter needs a swift resolution to the battle with Musk in order to limit the uncertainty for its shareholders, employees and customers, and any fallout for its business that could be exacerbated by costly, prolonged litigation.

Although Tuesday's hearing is largely a procedural one, it could offer a look at how each side will approach what is likely to be a messy litigation process. It may also provide a glimpse as to how the judge overseeing the case, Delaware Court of Chancery chancellor Kathaleen St. Jude McCormick, is approaching the dispute.

"There may be hints from what she asks and what she says, and what they say, during the hearing that may tell us something," said Carl Tobias, a professor at the University of Richmond School of Law.

The case has already hit a small snag: While the hearing was originally scheduled to take place in-person, McCormick sent a letter to the two parties on Monday alerting them that she tested positive for Covid-19 and would be moving the hearing to Zoom.

Less than three months after the blockbuster acquisition deal was inked, Musk moved to terminate the agreement. He accused Twitter of breaching the deal by making misleading statements about the number of bot and spam accounts on the platform, and by allegedly withholding data Musk says he needs to evaluate the scale of the issue.

Twitter hit back last week in a 60-plus-page lawsuit alleging that it is Musk who has violated the agreement. In the suit, Twitter suggested Musk is using bots as a pretext to try to exit a deal over which he now has buyer's remorse, following the market downturn that has tanked Twitter shares, as well as those of Tesla, which the billionaire is relying on in part to finance the deal.

Twitter asked the court to compel Musk to complete the deal to buy the company. While many legal experts say Twitter likely has the stronger argument in the dispute, some also expect the company may end up settling with the billionaire if the case starts to drag on, in an effort to reduce the disruption to its business.

As with the dispute generally, Twitter and Musk appear far apart on whether to have a speedy trial. In its motion, Twitter said the expedition is necessary to ensure the deal can be completed prior to the "drop dead" date of October 24 that the two sides previously agreed to close the deal by, and to "protect Twitter and its stockholders from the continuing market risk and operational harm resulting from Musk's attempt to bully his way out of an airtight merger agreement."

In a Friday court filing, Musk's lawyers called Twitter's request an "extreme expedition" and claimed that the dispute is "extremely fact and expert intensive, requiring substantial time for discovery." They also claimed that the original agreement stipulated that drop-dead date would no longer apply if one party filed litigation over the deal, calling Twitter's request "moot," and asked that the trial be scheduled for on or after February 13, 2023.

McCormick likely will not decide on whether to expedite the proceedings during the hearing Tuesday, according to Tobias, but rather will consider both sides' arguments and how long it could take to prepare for trial, including producing discovery and coordinating expert testimony, and then issue a decision at a later date.

"I think she's going to try to work toward something that is reasonable in light of the complexity" of the dispute, Tobias said. "This court has a great reputation for resolution of this kind of litigation, and so she'll be especially careful to give [both sides] the best treatment possible."

Meanwhile, Twitter continues to take the steps necessary to proceed with the acquisition. The company on Friday sent a letter to shareholders inviting them to vote on the deal to sell Twitter to Musk for $54.20 per outstanding share at a special meeting on an undisclosed date and time later this year, according to a regulatory filing. Twitter's board previously unanimously recommended that shareholders vote in favor of the deal, a position it reiterated in the letter.

Despite Musk's move to terminate the deal, "we are committed to closing the merger on the price and terms agreed upon with Mr. Musk," the Friday letter states. "Your vote at the special meeting is critical to our ability to complete the merger."