(CNN) An agitated President Donald Trump on Tuesday branded the Democratic impeachment process a "lynching" shortly before a crucial new witness is scheduled to give a deposition that could potentially unpeel new layers of the Ukraine scandal that is threatening his presidency.

Bill Taylor, the top US diplomat currently in Ukraine, is due at a closed-door session of three House committees and plans to fill in the gaps of his text messages with US diplomats about Ukraine, a source familiar with his testimony told CNN's Jeremy Herb and Kylie Atwood. That'll offer new material for an ever-broadening investigation now threatening to dash Democratic hopes of swiftly wrapping up the entire impeachment process.

Taylor will be asked about increasingly firm evidence that Trump was running an off-the-books foreign policy operation in Ukraine for personal political gain in a possible abuse of power.

He arrived in Washington amid an evolving political environment. Half of all Americans now say Trump should be impeached and removed from office, according to a new CNN/SSRS poll . That's a new high in CNN polling on the topic and the first time that support for impeachment and removal has significantly outpaced opposition.

Trump, who on Monday called on Republicans to be tougher in his defense, warned in a tweet that Democrats were setting a precedent that a president of their own party could be impeached in future without due process.

"All Republicans must remember what they are witnessing here -- a lynching. But we will WIN!" Trump wrote.

Trump's use of sharp racial language got a swift reaction from his opponents on Capitol Hill.

Congressional Black Caucus Chairwoman Karen Bass told CNN that Trump's lynching tweet is consistent with his pattern of throwing out "racial bombs" to throw "red meat" to his base when his back his against the wall. Rep. Harley Rouda, a California Democrat, called Trump's tweet "offensive."

It was impossible to judge the President's motivations for sure. But it would not be the first time that the President has stoked a fierce controversy to take attention away from an event -- in this case Taylor's appearance -- that could be politically damaging for him.

Political pitfalls for Democrats, too

Paradoxically, the mountains of new evidence collected in recent days -- mostly from depositions by career State Department officials -- also threaten to make impeachment a more perilous political exercise for Democrats.

A torrent of disclosures could dash hopes for a swift House vote on articles of impeachment before the Thanksgiving break as members follow fresh paths of inquiry beyond the original scope of questioning. That could in turn also hinder their effort to offer the public a crisp, easily understandable case against a President who habitually defies limits on his power.

CNN reported Monday o n growing expectations that historic votes on impeachment may now slip towards the end of the year -- even as Democrats also move to begin doing weekend work with a scheduled Saturday deposition for another State Department official.

Such a scenario would make it more likely that a subsequent Senate trial of the President could overshadow and infect the Democratic Party's presidential primary votes early next year, a time when party leaders hope voters will focus instead on considering their own candidates for President.

During Bill Clinton's impeachment process, for instance, it took two months between the House Judiciary Committee voting on Articles of Impeachment for him to be acquitted in the Senate.

One option would be for Democrats to give up on building a broad case against Trump and rely mainly on recent testimony and a whistleblower report on Trump's behavior and a rough transcript of his July 25 call with Ukraine's President Volodymyr Zelensky.

Many Democrats believe that there is sufficient evidence in those documents alone to prove that Trump abused his power and committed high crimes and misdemeanors by trying to coerce Kiev into providing dirt on possible Democratic nominee Joe Biden.

But such an approach risks depriving the public of the full scope of the President's alleged wrongdoing, weakening the case and easing pressure on Republican senators defending him.

"There is a debate now -- should we have a narrow inquiry or a broad one?" said Corey Brettschneider, author of "The Oath and the Office: A Guide to the Constitution for Future Presidents."

"The choice I do think they shouldn't make -- is a narrow inquiry. They don't want to miss the many abuses of power that are going on here."

Votes could slip until the end of the year

Given that Democrats appear far from wrapping up private depositions, may want to call new witnesses from multiple agencies, hope to publish transcripts of hours-long depositions and also want to hold public hearings, it is tough to see them advancing Articles of Impeachment in the committee next month.

As a case in point, the top US diplomat currently in Ukraine Bill Taylor is scheduled to deliver a deposition to three House committees on Tuesday. The US charge d'affaires in Kiev was depicted in text message exchanges with the President's men as saying it would be "crazy" to withhold military aid to the former Soviet state to coerce it into offer political favors. So he's potentially a critical witness for impeachment managers.

Other officials are also on the deposition list in the coming days. And testimony last week by Trump's former top Russia hand Fiona Hill -- that for the first time exposed the depth of Trump's Ukraine operation -- raised the possibility that former national security adviser John Bolton could be called for blockbuster testimony.

Even a delay of weeks on the tight self-imposed impeachment timetable could have significant knock on effects.

It now seems all but inevitable that at the time when Democrats hoped to focus voters on plans for health care reform, lowering student debt and a fairer economy in the run up to the Iowa caucuses in February, the nation's attention will still be fixated on Washington.

Republicans could face political consequences too

A prolonged impeachment saga could begin to test public patience for the decision by House Speaker Nancy Pelosi to proceed with impeachment in the first place and erode Democratic leverage and even cause a voter backlash.

It could also give Trump more time to unleash his disinformation campaign in alliance with conservative media to discredit the investigation — as he did effectively with the Mueller probe.

If the increasingly complicated case against Trump makes a swift denouement impractical, Democrats may begin to doubt Pelosi's decision to hold off on impeachment months ago -- after the special counsel provided what some scholars see as strong evidence of obstruction of justice. Trump's defenders could soon begin to make the case soon that a decision to overturn an election should best be left to voters due to weigh in months, rather than lawmakers on Capitol Hill.

But Democrats will not be alone in facing dangerously shifting political currents should impeachment drag on longer than expected. After all, every week that has passed since Pelosi fired the starting gun a month ago has weakened Trump's position.

It's possible that day after day of damaging disclosures about Trump's off-the-books dealings with Ukraine to get dirt on Biden could significantly weaken the President's position.

That might not just begin to turn public opinion -- increasingly in favor of at least investigating the President -- it could considerably increase the political price that GOP senators will pay to save the President in a Senate trial.

Vulnerable Senate GOPers like Maine's Susan Collins and Colorado's Cory Gardner won't welcome delays that could leave a vote to acquit Trump fresh in voters' minds next November.

Events of the last few days -- over Trump's aborted plan for a G7 summit at his Florida resort and his Syria withdrawal -- have exposed increasing GOP impatience with the President.

While there is no suggestion that his Senate firewall is in danger of collapsing, it appears that Trump will continue to fray tempers in the months before a Senate trial.

"We have to get tougher and fight," Trump warned his party on Monday in a wild hour-long photo-op before a cabinet meeting.

Appropriate behavior for a President facing impeachment might be to act in a way designed to cause his own party the minimum possible embarrassment. That's not Trump's way.

He caused more cringing on his own side by blasting th e "phony" emoluments clause o f the Constitution and by taking George Washington's name in vain on Monday.

Many more weeks before a Senate impeachment trial bring the possibility that the incorrigible President could commit more conduct that could add to the case against him.

While Republicans many not break against Trump after months of political pressure, he's bound to infuriate his own side even more as the bitter historic pill of impeachment beckons.

"(There is) growing frustration in the Republican Party, growing disenchantment in the Republican Party, but we haven't seen a real breakout and we may not see one through this process," David Gergen, an adviser to GOP and Democratic presidents who is now a senior CNN political analyst, told CNN International on Monday.