House Speaker Nancy Pelosi (D-Calif.) brushed aside a question about the pending Senate impeachment trial against President Trump, pointing to a different set of Democrats who were in charge.

“I have appointed the managers. You’ve haunted me, tracked me — ‘Who are they? When are they coming?’ — well, they’re here and they have a responsibility and I’m very confident in how they will proceed,” Pelosi told reporters Thursday.

These House managers face a very difficult challenge, with the jury stacked against them. With 53 Republicans in the Senate, chances of winning a conviction against Trump will be impossible unless 20 or more GOP senators break ranks.

So the Democrats enter the trial with lower-level goals to, at a minimum, represent a political victory by convincing the public of presidential malfeasance and inflicting pain on Republicans from swing states.

Their initial goal is to find at least four GOP senators who believe more witnesses should be called, particularly John Bolton, Trump’s former national security adviser who parted ways with the president on bad terms. He is willing to testify, if subpoenaed, about his knowledge of the “drug deal” — his description, according to onetime White House aide Fiona Hill, of the campaign to pressure Ukrainian leaders to investigate Trump’s domestic political rivals.

As the managers make this pitch, they have to be very careful that they do not undermine the quality of the House’s investigation into the scandal. There’s a danger that the more they demand witness testimony, the more their basis for voting to impeach Trump last month on charges of abuse of power and obstruction of Congress looks as if it were an incomplete product.

Ultimately, if Republicans are set on blocking more witnesses and acquitting Trump, these managers have to make sure they deliver their case in an easy-to-understand fashion so that voters will agree with Democrats who accuse the Republicans of covering up wrongdoing.

Those goals each require a separate and distinct pitch, focused on a different audience and a different type of focus. It’s one of the trickiest balancing acts possible for a group that only started working together a couple days ago, when Pelosi announced the group.

These seven managers comprise the chairmen of the House Intelligence and House Judiciary committees — Reps. Adam B. Schiff (D-Calif.) and Jerrold Nadler (D-N.Y.), respectively — as well as three others who serve on Nadler’s panel, one who serves on both committees and another who does not serve on any committee of jurisdiction.

According to their aides, they expect to assemble in the Capitol on Sunday for a strategy session. They will meet again Monday for both strategizing and a walk-through of the reconfigured Senate chamber so they will know where to sit and stand.

On Tuesday, the House managers will take their seats at a specially designed table on the left side of the well of the chamber, with the president’s team seated at a similarly curved table on the right side.

Just after 1 p.m., Senate Majority Leader Mitch McConnell (R-Ky.) will offer his resolution for the parameters of the trial. Then, the two legal teams get to debate for two hours, before Democrats get to offer amendments to that GOP resolution.

Eventually, McConnell’s outline will pass, as all 53 Republicans have said they support it, and then the House managers will most likely begin presenting their case Wednesday.

The odds against them can best be explained by this fact: Even if they prove every fact of their case, quite a few Republicans contend that Trump had every right to withhold $391 million in security aide from Ukraine until corruption investigations were conducted.

Sen. Rand Paul (R-Ky.) dismissed Thursday’s ruling by the Government Accountability Office, an independent agency that reports to Congress, that the president violated the law by delaying funds that had been legally approved by lawmakers.

“The strange thing about it is, they’re saying that you can’t withhold money for policy reasons,” Paul told reporters, pointing to the annual Pentagon policy bill that regularly requires Ukraine to meet certain anti-corruption standards before foreign aid can be released. “So I think presidents withhold money all the time, move money around. I think there’s a great deal of latitude to what presidents do.”

To that end, the House managers need to present as much evidence as possible toward Trump’s motivation in delaying the aid, because almost every Republican accepts the fact that the president was the main force behind the delay.

Expect to see some focus on Gordon Sondland, the ambassador to the European Union who testified before Schiff’s committee that Trump focused on making sure there was a public announcement of an investigation related to Hunter Biden’s activities as a board member of a Ukrainian energy company, not necessarily that an actual investigation happened.

That undercuts the defense that Trump cared about rooting out corruption and just wanted political fallout for the son of former vice president Joe Biden, a leading 2020 rival to Trump.

In their bid to win more testimony, Schiff and Nadler are going to have to tailor their pitch to a smaller group of Republicans who have indicated publicly that they are open to hearing testimony. That list always includes Sens. Susan Collins (R-Maine), Lisa Murkowski (R-Alaska) and Mitt Romney (R-Utah), but some Democratic advisers say there is a broader collection of older GOP senators who are retiring this year or a few years from now.

If enough of those veteran Republicans feel they need to hear more evidence, it could force McConnell into a broader negotiation over which witnesses to call and whether each side gets to call witnesses.

But there is likely to be a two-step vote on witnesses, first a generic vote about whether to hear more evidence and, if that passes, a series of votes on which witnesses and which documents should be produced.

There’s the possibility the Senate votes to approve hearing witnesses, in general, but then never votes to approve a specific witness.

All these obstacles require such a delicate dance by the managers, while they continue to defend the overall impeachment product from last month while at the same time condemning Republicans for not wanting to hear more evidence.

“They don’t want to hear from eyewitnesses. They don’t want to — they want to ignore anything new that comes up,” Pelosi said Thursday. “We saw a strong case, an infallible, undeniable case for the impeachment of the president.”