Congress has reached the ultimate stonewall: The White House said Tuesday that it won’t cooperate with the impeachment inquiry at all. That means key witnesses such as diplomat Gordon Sondland, who was working on behalf of President Trump in Ukraine, won’t share what they know about Trump’s attempts to get Ukraine to investigate his political opponents.

So what does Congress do from here? We are in uncharted territory as far as the Constitution goes. House Speaker Nancy Pelosi (D-Calif.) will hold a call with House Democrats on Friday, days before they return from a two-week recess, to discuss strategy. Here are three key questions that could determine what their next move is.

1. Will a public-relations campaign work to pressure Trump?

Democrats launched such a campaign in September to get the whistleblower report. It seemed to work, because they got it — and so did the public. The Trump administration blocked Sondland hours before he was set to testify Tuesday. It’s probably not a coincidence that later that morning, Democrats made sure to dangle something intriguing that was lost with his testimony: Sondland also had texts and/or emails on his private phone that the State Department had confiscated. “Those messages are also equally relevant to this investigation and the impeachment inquiry,” House Intelligence Committee Chairman Adam B. Schiff (D-Calif.) told reporters.

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Polling suggests public opinion has shifted in Democrats’ favor since the inquiry was announced. A new Washington Post-Schar School poll shows 58 percent of Americans say that the House was correct to open the inquiry. There’s even increasing Republican support for impeaching Trump. If those numbers tick up further, could Trump feel enough pressure to start allowing his administration officials to testify and hand over documents?

2. Does anyone else come forward?

People of high interest include the former U.S. ambassador to Ukraine, Marie Yovanovitch, whom Trump removed from her post this spring. Then there’s Bill Taylor, the acting ambassador to Ukraine. In texts, he expressed concern that they were setting up a quid pro quo before Trump’s July call with Ukraine’s president.

Sondland said he was willing to testify — he even flew from his post in Brussels to Washington before the State Department pulled the plug.

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Congress also still hasn’t talked to the first whistleblower. Democrats are trying to get this person to testify and are considering having the person do it from a remote location and obscuring the individual’s image and voice. And now there’s a second whistleblower whose attorneys say can share firsthand information.

But almost all of these people risk their careers by talking, given the Trump administration’s blanket ban on working with the impeachment inquiry. A former Trump diplomat in Ukraine, Kurt Volker, testified only after he abruptly resigned from the Trump administration.

3. Will the House just drop the Ukraine investigation and impeach Trump for obstruction of the probe?

House Democrats can certainly do that. The Constitution lets Congress impeach a president for any reason it deems fit, because Congress gets to decide what “high crimes and misdemeanors” in the impeachment clause are. If it decides blocking Congress from its oversight duties meets that requirement, then so be it. A similar article of impeachment was written up against President Richard M. Nixon and voted out of the House Judiciary Committee.

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But as I wrote here, how it plays politically is another question. Democrats would be at risk of pursuing impeachment of a president without a comprehensive investigation of what he did. As it stands now, there is no evidence that Republican senators would break with Trump and vote to remove him from office. Democrats would like more time and evidence to build their case and make this impeachment process bipartisan. They may not get to do that.

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