"Democrats have to stay very disciplined in adhering to that clear, cogent narrative that was written for us,” Rep. Gerry Connolly (D-Va.) said. "Their strategy of stonewalling and obstruction is significantly counterproductive and frankly puts them in further legal peril — not only the president but his minions."

But Trump’s anti-impeachment offensive — a mix of legal, political and personal attacks, some logical and some simply bombastic — poses a real challenge for Democrats. Nearly three years into Trump’s presidency, lawmakers are still trying to figure out how to respond to a president who knows few, if any, limits in his behavior or rhetoric.

Trump has long resisted Democrats’ investigations, routinely ignoring subpoenas for documents and witness testimony and exposing the inherent weaknesses of Congress’ oversight powers.

Even as Democrats have moved into a new investigative phase with their rapidly-advancing impeachment inquiry, Trump has shown no signs of letting up, ensuring the constitutional clash will only ratchet up.

Still, Democrats believe their case against the president over the Ukraine scandal, this time, is unassailable — a controversy that even Republicans can't ignore. And it’s reinforced not only by closed-door testimony by senior officials, but by Trump’s own comments on the White House lawn.

“You saw when he stood out there and tried to say, not only should Ukraine investigate, but China should,” said Rep. John Yarmuth (D-Ky.). “I don't think there’s any question we’ve got him on the run at this point.”

The proof, Democrats say, is in the polling figures that are rapidly rising in Democrats’ favor. Two separate polls released Tuesday by the Washington Post and Quinnipiac showed a significant uptick in public support for impeachment, including among independents and Republicans, with a majority of those surveyed in favor of Democrats’ inquiry.

“If you look at the polling, we’ve so far kept the momentum going,” Yarmuth said.

But Democrats acknowledge that they have for years failed to pin Trump down. For every seemingly career-ending scandal of his presidency — including damning findings in the Mueller report, hush money payments to adult film actresses and numerous accusations of self-dealing — public sentiment has barely budged.

"It’s not that it’s difficult to message against him," one Democratic aide said. "What’s difficult is that he’s obviously the president, so whatever he says is quoted as the headline. That’s the difficult part."

Yet the Ukraine scandal is different, Democrats insist. The controversy is clear — Trump abused the power of his office for political gain — and there’s more than enough evidence that is already public.

Even with the White House stonewalling, Democrats have been making progress in investigative work — securing testimony from three people central to the Ukraine controversy in two weeks. And lawmakers say they expect more to leak out as it becomes evident how many people at senior levels of government were disturbed by Trump’s call.

The White House itself has also released some information on the president’s July 25 call to Ukrainian President Volodymyr Zelensky and Trump’s efforts — along with his personal lawyer, Rudy Giuliani, and other officials — to pressure Ukrainian officials to dig up dirt on Biden while withholding U.S. aid.

Acting Director of National Intelligence Joseph Maguire testified before the House Intelligence Committee and defended the rights of an anonymous whistleblower to come forward; the Intelligence Community Inspector General Michael Atkinson also backed up the whistleblower's actions. Since then, a second whistleblower has reportedly emerged as well.

And Trump was unable to stop politically damaging text messages from being revealed by former U.S. special envoy to Ukraine Kurt Volker that raise the question of whether there was a "quid pro quo" between the Ukrainians launching a Biden probe and receiving the U.S. aid. Volker denied that link in his own testimony.

Still, there have been setbacks. The White House has refused to comply with several Democratic subpoenas or requests for testimony, including from Giuliani, Vice President Mike Pence, Secretary of State Mike Pompeo, and the latest, U.S. Ambassador to the European Union Gordon Sondland, a key figure in the scandal.

Democrats say they won’t be deterred by the administration’s blockade.

“Impeachment grows more likely every day, and every act of obstruction and defiance by the executive branch becomes part of the issue of obstruction, which, itself, is a count for impeachment. They really are digging their own ditch,” said Rep. Jamie Raskin (D-Md.), who sits on the House Judiciary Committee.

But lawmakers also fear the takeaways from their hard-fought investigations could be buried with a single Trump tweet if they don’t stay focused.

“We’re going to show extreme message discipline in talking about this explosive narrative,” Raskin said.

Trump and GOP congressional leaders, meanwhile, have ramped up their attacks against Democrats and the impeachment inquiry itself.

Trump called it a "kangaroo court" on Tuesday in explaining why he wouldn't let Sondland testify before Congress. House Minority Leader Kevin McCarthy has slammed Pelosi for rejecting calls for a full House vote to authorize the impeachment inquiry, which took place during the Nixon and Clinton impeachments.

Trump has also gone on Twitter to rant against Pelosi, House Intelligence Committee Chairman Adam Schiff, the anonymous whistleblower and even GOP Sen. Mitt Romney, who dared to "raise concerns" about Trump's interactions with Ukrainian officials. Trump called Romney a "pompous ass," and implausibly suggested the Utah Republican should be impeached.

Democratic leaders have been careful not to hit back at Trump for every Twitter attack. Instead, Pelosi and her top deputies have urged their caucus to keep the message squarely focused on what they see as a clear abuse of power and attempt to undermine U.S. elections.

“[Trump’s] snubbing his nose at the vision of our founders, his disloyalty to the Constitution is something we have to study, and it's just with the facts,” Pelosi said at an event in Washington State on Tuesday. “The facts and the Constitution, that's what it's about. It's not about any other disagreement you may have in an election.”

In a conference call last week, Democratic Caucus Chairman Hakeem Jeffries encouraged lawmakers to use “repetition,” relying on six key words — “betrayal, abuse of power, national security” — to hammer their point to the public.

“The challenge won’t be how do we keep this in the public mind,” Connolly said. “He is so overreacting, and badly, to these developments that I think even if we were to go dark — which we won’t — he won’t.”