After Secretary of State Mike Pompeo’s angry refusal Tuesday to allow State Department officials to testify before a House of Representatives committee about Ukraine, congressional Democrats face a newly urgent question: What legal tools does Congress have to compel the Trump administration to provide testimony and documents?

This fundamental constitutional question may begin moving gradually toward the Supreme Court in coming months, perhaps slowing the Democrats’ timeline for impeachment proceedings. For such a confrontation between the legislative and executive branches probably can only be resolved by the third leg of our government, the judiciary.

Much as the Watergate investigation of President Richard M. Nixon turned on the production of White House tape recordings of Nixon’s conversations in the Oval Office, the Trump investigation may cross a similar threshold. A House committee chaired by Rep. Adam Schiff, D.-Calif., is seeking to gather evidence to assess an allegation by a CIA whistleblower that “the president of the United States is using the power of his office to solicit interference from a foreign country in the 2020 U.S. election.”

But how will Congress seek to compel testimony it has requested from Pompeo and five other current and former State Department officials about Ukraine, after Pompeo’s defiant rejection? The secretary of state added his own fuel to the fire, calling the request an attempt “to intimidate, bully, and treat improperly” the officials who had been summoned. (Pompeo ignored the fact that two of the Ukraine experts, former ambassadors Kurt Volker and Marie Yovanovitch, had told House investigators they were fully ready to cooperate.)

Schiff’s staff refused to discuss legal options with me Tuesday. But the legal pathways ahead are clearly outlined by attorneys who have examined the parameters of congressional investigations and the legal remedies for enforcing. Discussions with several of these legal experts and a review of law-review articles and books on the topic yield some basic guideposts.

A simple summary is that it isn’t easy for Congress to compel executive branch testimony. Congress can subpoena witnesses. Yet if the witness refuses to testify, and the House votes that he’s in contempt of Congress, what remedy exists to enforce the contempt finding? Scholars cite three legal avenues that could be pursued. But all are problematic.

First, the House could try to enforce a contempt finding on its own. The Supreme Court affirmed in 1821 that Congress’s contempt power, like its authority to investigate and subpoena, is inherent in the Constitution’s grant of legislative functions. So, in theory, the House could order its sergeant at arms to arrest the recalcitrant witness.

But exercising this power could lead to a much worse constitutional crisis. Imagine the sergeant at arms arriving at the State Department with handcuffs for Pompeo, and finding the way blocked by armed Diplomatic Security officers. This “Seven Days in May” scenario is implausible, even in Trump’s Washington.

A second pathway would be for the House to use an 1857 statute that allows criminal prosecution of a witness who refuses to comply. The problem is that the prosecution would be in the hands of Trump’s Justice Department, controlled by Attorney General William P. Barr, who was named in the whistleblower’s complaint. If Barr recused himself, a Trump-appointed U.S. attorney might still refuse to present the contempt allegation to a grand jury. And even if the grand jury returned an indictment on its own, the U.S. attorney could decline to sign or prosecute it.

The third avenue is a lawsuit to enforce congressional subpoenas, and this is the one that scholars say would probably be most appropriate, even though the case could take months. Even if Congress asked for an expedited summary judgment by the district court, that decision would almost certainly be reviewed by an appeals court before the decisive Supreme Court ruling.

This legal fight would slow the impeachment process, which has its plusses and minuses for Democrats. The stall might anger voters, but Democrats could argue that it was the Trump administration that was dragging its feet and refusing cooperation, even as the Democrats pressed for testimony and documents to resolve the inquiry.

The road ahead is obscured, and the epic constitutional battle I’m describing may never happen. But we know after Tuesday’s letter from Pompeo that the Trump team has circled its wagons. Trump, his vice president, his secretary of state, his attorney general and his chief of staff were involved, to some degree, in the Ukraine matter. And they don’t appear in a mood to retreat or surrender.

— David Ignatius is a columnist for Washington Post Writers Group.