"He's going to make a report, I think to the attorney general and to Congress," Trump told reporters earlier this week of Giuliani. "He says he has a lot of good information. I have not spoken to him about that information."

Even on Thursday, as the Judiciary Committee finalized the House's articles of impeachment, Trump retweeted smears of former U.S. Ambassador to Ukraine Marie Yovanovitch, whose unceremonious ouster by Trump in May formed an important chapter of Democrats' impeachment case.

In other words, Democrats are facing the prospect of impeaching a president as he dismisses their allegations in real-time. But that's no reason to hesitate, they say, even if Trump appears certain to win an acquittal in the Republican-controlled Senate.

“Should we stop stopping speeders if they still speed?” wondered Val Demings (D-Fla.), a member of the Judiciary and Intelligence Committees. “When we vote, we will have done our job. Then the Senate needs to take these matters seriously and take action.”

“The behavior is the president’s. The blame is on the president. We are not responsible for that,” said Rep. Madeleine Dean (D-Pa.), another Judiciary Committee member. “If he continues in that behavior, we hope the Senate will do their duty.”

A post-impeachment Congress will present a tricky dynamic for Democrats, who are still working to ink a series of high-profile legislative deals with Trump while vowing to continue an aggressive set of investigations against him, though this time without the threat of impeachment as a cudgel.

Several House committees are deep into legal battles to obtain the president’s personal financial records. The House is also engaged in numerous court cases meant to force the release of these documents as well as compel the production witnesses and evidence connected to special counsel Robert Mueller’s probe that the White House has blocked from lawmakers. Two of those court cases will be heard by a federal appeals court on Jan. 3.

Another series of favorable court rulings over the next few months could net Democrats reams of embarrassing materials and witnesses that could add new layers to their case against Trump. That prospect has led to scattered calls for the House to slow down its inquiry and await the documents, though senior Democrats have largely dismissed any delays as too risky.

Separately, House Intelligence Committee Chairman Adam Schiff has vowed to continue his panel’s Ukraine investigation, even when it’s no longer in the context of impeachment, though the White House is still signaling that that it will continue to throw up more roadblocks once impeachment is over.

Democrats also cite polls showing Americans, in a bipartisan way, reject Trump’s conduct toward Ukraine even if the public is more evenly divided about the prospect of impeachment. The lawmakers leading the impeachment inquiry see it as a vindication of their efforts in a starkly divided political moment, and suggest it points toward the need for more oversight of the president in a post-impeachment Congress.

In fact some lawmakers say the impeachment drive has already been successful in halting Trump’s malign ambitions.

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“There’s absolutely no question that had we not launched this investigation he would have successfully extorted Ukraine and right now, you guys would be writing about the Ukrainian investigation of allegations of corruption against Joe Biden’s family,” said freshman Rep. Tom Malinowski (D-N.J.), a former State Department hand who hails from a district Trump won in 2016.

“I do believe that the process and the likely outcome will serve as a deterrent,” he added. “We would be in a much, much worse situation if Congress of the United States threw up its hands.”

Other influential Democrats say they’re still placing their hope in Senate Republicans even though many have all but declared their intent to acquit Trump of the charges against him.

“The only way we’re going to stop him from continuing this is to convict him in the Senate and remove him from office,” said Rep. David Cicilline (D-R.I.), a member of House leadership.

“If this president is not held accountable and my Republican colleagues in the Senate don’t honor their oath of office and convict him based on overwhelming evidence,” said Cicilline, “we will no longer have a democracy.”