The House Democrats who will make the case for President Trump’s removal from office face a rapid briefing schedule and uncertain trial rules before squaring off against Trump’s defense team on Tuesday for the first time in their four-month investigation.

The seven impeachment managers face multiple challenges as they take their case out of the confines of the House and into the Republican-controlled Senate. For one, they are facing a skeptical, if not openly hostile, jury in the 53-seat GOP majority that will be able to set the rules of engagement for the trial.

While Senate Majority Leader Mitch McConnell (R-Ky.) has indicated that he plans to use the 21-day trial of President Bill Clinton in 1999 as a model, he has yet to detail the rules for the Trump trial.

Those rules will be debated Tuesday — not by senators but by the House managers and the White House defense team in what stands to be a preliminary dispute ahead of a high-stakes period of arguments for and against the first removal of a U.S. president from office in history. Removing Trump requires two-thirds of the Senate.

Though Trump’s team will try to pave the way for a swift acquittal, the Democrats face a more complex task.

According to House aides working on the impeachment case, the seven managers — led by Intelligence Committee Chairman Adam B. Schiff (D-Calif.) and Judiciary Committee Chairman Jerrold Nadler (D-N.Y.) — are to meet through the long Martin Luther King Jr. Day weekend along with dozens of staff members.

They are seeking a conviction, but with all but a handful of Republicans publicly skeptical of Trump’s removal on the basis of the current evidence, they must first as a threshold matter persuade four Republicans to join with the 45 Democrats and two independents who caucus with Democrats to extend the trial by admitting additional witness testimony and documents.

They also must balance the need to appeal solely to the audience of 100 before them while also making the case to the public about the seriousness of the president’s conduct — which, they believe, could in turn influence the votes of some key senators.

“Ultimately, the American people are going to make their voices heard to the members of the United States Senate and insist that these proceedings not be a coverup,” said Rep. David N. Cicilline (D-R.I.).

The managers will be able to draw on transcripts from more than a dozen extended depositions of key figures, hours of televised hearings and a trove of emails, text messages, and other documents. But huge gaps remain in the record: The Trump administration has resisted scores of document requests addressed to multiple Cabinet departments; some have begun to trickle out publicly through Freedom of Information Act requests but have not been formally provided to Congress.

Important witnesses, meanwhile, have refused to testify, including former national security adviser John Bolton, acting White House chief of staff Mick Mulvaney and several more junior officials who had knowledge of the decision to withhold nearly $400 million of military aid from Ukraine. Also unclear is whether documents and testimony from Lev Parnas, a businessman who worked with Trump lawyer Rudolph W. Giuliani on the Ukraine affair, will be allowed to testify in the Senate.

The House released more of the documents from Parnas last week.

A key challenge for the House managers will be balancing their case for Trump’s removal with their case for additional witnesses and documents. The two are in tension to some degree: Some Republicans have interpreted the call for additional evidence as an admission that the House impeachment case is incomplete — and hence insufficient to warrant Trump’s removal.

“It’s not our job to do your job,” said Sen. Kevin Cramer (R-N.D.) this week. “You’re the prosecutors. Why should we help you make a bad record complete?”

A Democratic aide working on the impeachment case who spoke on the condition of anonymity Friday to preview the managers’ strategy said they would indeed seek to make both cases in concert.

“Of course, you’re going to hear about the merits — an overwhelming case that warrants a conviction. There’s never been a president in American history who has been accused of conduct of this kind,” the aide said. But the managers will make the case that the Senate must summon additional witnesses and documents “in order to tell the whole story they need to hear.”

“The case is not a complicated one,” the aide added. “When the president invites a foreign government to announce investigations attacking a political opponent, he’s undermining our democracy. . . . We’re going to talk about the way that that threat is a direct assault on these two fundamental pillars of our democracy and our security.”

Even before the Senate decides whether to hear witnesses — a decision almost certain to be put off until after the opening arguments — the House Democrats could very well make Trump himself their star witness, putting on display his own remarks.

Preliminary rules adopted by the Senate last week allow for such “equipment as may be required to permit the display of video or audio evidence, including video monitors and microphones” for use by the managers team as well as the White House defense. Each side will also have use of two laptop computers — devices that are typically forbidden except on the clerk’s desk.

The possible division of labor among the managers, however, remains unsettled.

During the 1999 impeachment trial, House Judiciary Committee Chairman Henry Hyde (R-Ill.) led the 13-member team, reading the articles to the Senate to formally begin the trial, and delivering presentations at key junctures, including the closing argument. But he delegated considerable parts of the House case to other managers, who delved into testimony from individual witnesses and otherwise split up the House’s roughly 15-hour presentation.

In this trial, Schiff is playing Hyde’s role — reading the articles of impeachment to the Senate on Thursday — but he could, several Democrats said this week, be an even more dominant player in the trial. A former federal prosecutor and veteran of a previous judicial impeachment, Schiff has exhibited a mastery of the facts of the impeachment case — delivering, on several occasions, lengthy extemporaneous speeches attacking Trump’s fitness for office.

A second House aide working on the impeachment case would not say Friday whether all seven managers would be guaranteed speaking roles on the Senate floor but said each would have an important role on the prosecution team.

Several Democrats said this week that the prosecution has been somewhat hamstrung by not knowing the thrust of Trump’s defense. During the course of the House impeachment proceedings, Republican lawmakers led the charge — offering mainly political, not legal, arguments against Trump’s impeachment. The closest thing to a legal outline of Trump’s defense came in an eight-page Oct. 8 letter from White House Counsel Pat Cipollone that many legal experts found lacking in substance.

The House is to deliver a written brief of the prosecution case to senators on Saturday evening; the White House reply is due at noon Monday, with a House rebuttal due 24 hours later. The White House brief on Monday is likely to be the first substantial outline of Trump’s case, and senators are watching closely.