The Trump administration rolled the dice on impeachment Tuesday, stopping a U.S. ambassador from testifying to Congress and blasting top Democrats in an open letter.

But the likely effectiveness of Team Trump’s efforts to delegitimize the impeachment inquiry is in serious doubt amid opinion polls that show growing public support for the process.

A new NBC News/Wall Street Journal poll released late Tuesday afternoon showed 55 percent of Americans supporting either an impeachment inquiry or President Trump Donald John TrumpFederal prosecutor speaks out, says Barr 'has brought shame' on Justice Dept. Former Pence aide: White House staffers discussed Trump refusing to leave office Progressive group buys domain name of Trump's No. 1 Supreme Court pick MORE’s all-out removal from office. No American president has been ousted from office in that fashion, though President Nixon resigned in 1974 while facing such a scenario.

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The decision to prevent the U.S. ambassador to the European Union Gordon Sondland from testifying emerged Tuesday morning.

It will fuel concerns that the president and his allies have something to hide, and Democrats wasted no time making that case.

The upside for Trump is that the stymieing of Sondland could slow the inquiry down and suppress — for now — any damaging information in the ambassador’s possession.

Sondland was one of several U.S. diplomats involved in talks regarding Ukraine.

At the heart of the current furor is a July 25 phone call in which Trump pressed the president of Ukraine to mount an investigation into former Vice President Joe Biden Joe BidenFormer Pence aide: White House staffers discussed Trump refusing to leave office Progressive group buys domain name of Trump's No. 1 Supreme Court pick Bloomberg rolls out M ad buy to boost Biden in Florida MORE, who is a leading 2020 presidential contender, and his son Hunter.

In texts that emerged last week, Sondland insisted to another U.S. official that there was no “quid pro quo” linking military aid to Ukraine with such an investigation. But he also told that other official — William Taylor, the U.S. chargé d’affaires in Ukraine — to stop discussing the matter via text.

Sondland had been due to testify before three House committees on Tuesday but those plans were undone by instructions from the State Department at the last minute.

A statement from Sondland’s lawyer, Robert Luskin, asserted that he was “profoundly disappointed” and that he “stands ready to testify on short notice, whenever he is permitted to appear.”

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House Democrats almost immediately announced they would seek to subpoena Sondland.

Others in the party argue the administration has miscalculated its response since, they say, the blocking of Sondland looks so suspicious.

“People aren’t buying this. They smell a rat,” said Karen Finney, a Democratic strategist who was the senior spokeswoman for 2016 presidential nominee Hillary Clinton Hillary Diane Rodham ClintonBloomberg rolls out M ad buy to boost Biden in Florida Hillicon Valley: Productivity, fatigue, cybersecurity emerge as top concerns amid pandemic | Facebook critics launch alternative oversight board | Google to temporarily bar election ads after polls close Trump pledges to make Juneteenth a federal holiday, designate KKK a terrorist group in pitch to Black voters MORE. “It’s hard to see how the White House will explain this, because you would think that if you have nothing to hide, you would have the ambassador go and testify.”

On Tuesday afternoon, the White House released its letter to Speaker Nancy Pelosi Nancy PelosiDemocratic senator to party: 'A little message discipline wouldn't kill us' Overnight Health Care: New wave of COVID-19 cases builds in US | Florida to lift all coronavirus restrictions on restaurants, bars | Trump stirs questions with 0 drug coupon plan Overnight Defense: Appeals court revives House lawsuit against military funding for border wall | Dems push for limits on transferring military gear to police | Lawmakers ask for IG probe into Pentagon's use of COVID-19 funds MORE (D-Calif.) and three key committee chairmen in which counsel Pat Cipollone accused the Democrats of pursuing impeachment in a way “that violates fundamental fairness and constitutionally mandated due process.”

The letter added, “Put simply, you seek to overturn the results of the 2016 election and deprive the American people of the President they have freely chosen.”

That kind of phrasing is a slightly more nuanced way of accusing the Democrats of participating in a “coup” — an incendiary charge that Trump has already leveled on Twitter.

Other allies backed up that message. Brad Blakeman, a veteran of President George W. Bush’s White House and a strong supporter of the current president, told The Hill that Trump was “right to push back,” adding that the administration should not “play into the hands of this kangaroo court.”

Rep. Jim Jordan James (Jim) Daniel JordanHouse panel pulls Powell into partisan battles over pandemic Sunday shows preview: Justice Ginsburg dies, sparking partisan battle over vacancy before election House passes resolution condemning anti-Asian discrimination relating to coronavirus MORE (R-Ohio), one of Trump’s fiercest advocates on Capitol Hill, told reporters earlier Tuesday that House Intelligence Committee Chairman Adam Schiff Adam Bennett SchiffSchiff to subpoena top DHS official, alleges whistleblower deposition is being stonewalled Schiff claims DHS is blocking whistleblower's access to records before testimony GOP lawmakers distance themselves from Trump comments on transfer of power MORE (D-Calif.) was running an “unfair and partisan process.”

But whether that argument will fly beyond Trump’s base remains uncertain.

Outside experts argue that the refusal to let Sondland’s testimony go forward could itself bolster the case for impeachment, ultimately helping Democrats more than the GOP.

“It strengthens the case substantially, on two grounds,” said Allan Lichtman, a history professor at American University and the author of a 2017 book, “The Case for Impeachment.”

“One is obstruction of justice. The other is contempt of Congress,” Lichtman said, noting that the latter charge was one that President Nixon also faced.

Harry Litman, a former deputy assistant attorney general, said the decision to prevent Sondland from testifying “strikes me as obstructive conduct.”

Litman also noted how the decision to stop the testimony came at the 11th hour.

“I think it is a distinct possibility that he was being prepared to testify and the preparers realized it would be a debacle so they told the White House,” he speculated.

Whether that is true or not, the haste with which Sondland was blocked appears to have caused consternation even among Trump loyalists.

Bloomberg reported on Tuesday evening that key Republicans were “blindsided” by the decision and asked the president to ensure such a thing did not happen again.

Such message coordination could be the least of Trump’s worries, however, if public opinion continues to shift against him or more damning revelations emerge.

The Memo is a reported column by Niall Stanage, primarily focused on Donald Trump’s presidency.