If a small number of Republicans were to join Senate Democrats in voting to request witnesses or other measures that Schumer wants but McConnell opposes, an impeachment trial could reveal new facts that might embarrass the administration even if it doesn't face oblivion.
Last month, the House of Representatives voted for only the third time in history to impeach the president. Then something else unusual happened:
Nothing.
President Trump, members of Congress, much of Washington and millions of Americans effectively pushed pause on a once-in-a-generation political saga to take off for the holidays.
So for those just tuning back in for the first full workweek of 2020, nothing substantive has changed in the story — but that also means the coming month may churn into a whirlwind.
House Speaker Nancy Pelosi, D-Calif., still must transmit the articles of impeachment adopted on Dec. 18 to Senate Majority Leader Mitch McConnell, R-Ky.
And Pelosi also must announce which lawmakers will cross over to the other side of the Capitol and make the case against Trump as "impeachment managers" before a jury comprising the 100 members of the Senate.
But the speaker has said she won't send McConnell the articles or name managers until she's confident about the nature of the process that will take place in the Senate, which is itself still subject to negotiations between McConnell and Senate Minority Leader Chuck Schumer, D-N.Y.
The White House also has yet to name a team of attorneys to defend Trump.
Witnesses and procedures
Schumer and Democrats want to hear from witnesses in the Senate trial, including top administration officials who could talk about what they and Trump did in the Ukraine affair last year.
In remarks on the Senate floor Friday, McConnell said the trial should follow precedent set with President Clinton's impeachment trial two decades ago, and that "midtrial questions" like witnesses should be considered after opening arguments and questions from senators.
The majority leader added that if Democrats want more evidence in the record, they should have done a better job under Pelosi in the House.
"As House Democrats continue their political delay, they're searching desperately for some new talking points to help them deflect blame for what they've done," McConnell said.
Pelosi responded by accusing McConnell of "feebly" complying with Trump's "cover-up" of his "abuses of power."
Schumer also said Friday it appeared the two sides were no closer to reaching an agreement on how a Senate trial would proceed.
Republicans control the majority in the Senate and are expected to permit Trump to retain his office.
But the way that's done, and how quickly, isn't settled.
If a small number of Republicans were to join Democrats in voting to request witnesses or other measures that McConnell opposes, an impeachment trial could reveal new facts that might embarrass the administration even if it doesn't face oblivion.
Rules of the road
Republican senators don't agree on exactly how a trial for Trump should run.
Some of them haven't closed the door to witnesses. Others have suggested that Senate investigators might take depositions from witnesses behind closed doors.
And although McConnell has promised to keep in lockstep with Trump and the White House about procedure because he doesn't feel obliged to be objective, that hasn't sat well with a handful of his own members.
Alaska Sen. Lisa Murkowski and Maine Sen. Susan Collins, for example, have said they take their responsibilities as jurors seriously and don't want to pre-judge an impeachment case or be seen as a rubber stamp for the White House.
Speaking on ABC's This Week on Sunday, Schumer seemed to deliver a message directly to certain GOP senators: "I hope, pray and believe there's a decent chance that four Republicans will join us," he said. "If they do, we will have a fair trial."
Meanwhile, the underlying facts about the Ukraine affair have continued to evolve in press reports since last month.
The New York Times detailed efforts by top administration officials to persuade Trump to unfreeze the military assistance to Ukraine that was blocked for a number of weeks last year.
Trump wanted Ukraine's government to launch investigations he thought might help him in the 2020 election; Democrats charge the hold on $391 million in aid was attempted extortion.
The website Just Security also revealed messages between the Defense Department and the Office of Management and Budget that appeared to make clear the freeze on assistance was taking place at Trump's direction.
Schumer has argued those documents mean Republicans must agree to witnesses and a fair trial, "not a rigged process that enables a cover-up."
Political warfare
With the outcome of the Senate trial likely foreordained — Republicans use their majority to preserve Trump in office — both parties want to use the process most effectively for their political ends while it's running.
Trump goes back and forth about his objectives. One thing he and supporters have said is they see an opportunity to use what began as an impeachment of Trump as an impeachment of former Vice President Joe Biden and his family.
Trump and aides sought an investigation in Ukraine involving Biden's son Hunter's tenure on the board of a Ukrainian gas company and Republicans have relished the opening to attack both father and son.
Trump's Republican support in Congress appears unbreakable.
No Republicans voted to impeach him in the House and even if one or two senators were to join Democrats, it's "inconceivable" that the requisite 20 Republicans might break ranks, McConnell has said.
If that holds as expected, Trump and supporters have the time they'll control in the Senate trial to use in whichever ways make most sense to them politically without fear about the outcome.
Democrats are examining the trial through an inverse lens: Knowing they can't remove him, how much political damage, they wonder, can they do to Trump?
Pelosi echoed Schumer in arguing that the press reports since the impeachment vote have further strengthened the case for it: Not only are facts about the president's actions further established, his refusal to produce witnesses or documents is all the more unacceptable, they argue.
To the degree that Schumer and Democrats can tease out more facts about the Ukraine affair, they could try to sustain press and public interest and attempt to go on hurting Trump politically, even if they can't ultimately eject him.
All the same, the world will continue to turn; Pelosi implicitly acknowledged the limits of her own efforts by inviting Trump to deliver the State of the Union address in early February even as the impeachment story line wore on.
Presidents traditionally use that annual speech to outline priorities and preview their budget proposals for the coming year, so the speaker's invitation suggests she expects Trump and the administration will endure.
Also, the presidential race likely will continue unabated, with the awkward reality that several Democratic candidates — the Senate includes Elizabeth Warren of Massachusetts, Bernie Sanders of Vermont, Amy Klobuchar of Minnesota, Cory Booker of New Jersey and Michael Bennet of Colorado — will need to break away from campaigning to be present in Washington for Trump's trial.