The committees pursuing the investigation have remained at work — securing a string of lengthy closed-door interviews with current and former diplomats, subpoenaing crucial documents and otherwise showing progress toward elucidating Trump’s pressure on Ukraine to investigate former vice president Joe Biden and his son at a time when U.S. military aid was being withheld from the country.

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Meanwhile, federal judges handed Democrats multiple victories last week in decisions that lawmakers called the most significant cracks yet in the White House’s stonewalling. And facing constituents at home, many lawmakers said they have gotten more encouragement — or at least less backlash — than they might have anticipated as public opinion polls now show more Americans supporting impeachment.

“Donald Trump has been living in a house of cards, and it’s beginning to fall apart,” said Rep. Daniel Kildee (D-Mich.). “There was some anxiety — should we have stayed [in Washington]? … There was a little uncertainty about that. But I think we come back in a much stronger position.”

Said Rep. Ted Deutch (D-Fla.): “I think we’re much further along after two weeks away from Washington than people could have imagined.”

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There are still key unresolved questions: Should Democrats bow to Republican demands and take a formal vote authorizing an impeachment probe? Should the investigation of Trump extend into other alleged misdealings with foreign leaders? How quickly should the impeachment process come to a head?

But on the central question of whether Trump ought to be investigated for potentially committing high crimes and misdemeanors worthy of removal from office, Democrats are now largely united: Only seven of 235 House Democrats have stopped short of endorsing the impeachment inquiry, and the White House position, laid out in a letter sent to House Speaker Nancy Pelosi (D-Calif.) and three committee chairmen last week, has hardened the resolve of many Democrats.

Rep. Xochitl Torres Small (D-N.M.), who narrowly won a rural, GOP-held seat last year, wrote an op-ed in the Las Cruces Sun News endorsing an impeachment probe last week after staying mum on the subject for months. Failing to investigate, she wrote, would “risk our safety and the integrity of the very Constitution I swore to support and defend.”

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Rep. Jason Crow (D-Colo.), a freshman who wrested a suburban Denver district from GOP hands, said in an interview that some lawmakers who might have feared a backlash from launching an impeachment probe have instead seen the opposite effect.

“I think there is increased confidence, and that is a result of the response we’re getting in many of our communities,” he said. “Out in our district, people really do want the rule of law upheld. That’s certainly what I’ve been hearing.”

Republicans, meanwhile, have struggled to mount a coherent defense of the president. Trump’s leading House defenders have focused mainly on the process, accusing Democrats of violating precedent by proceeding without a formal House vote.

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While previous presidential impeachment investigations have included such a vote, it is not required under the Constitution, federal law or House rules. Several federal judges, for instance, have been impeached after investigations that were not previously authorized with a House vote.

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That makes the calculation of whether to further formalize the impeachment process a political one, and Democratic lawmakers and aides said they have seen little in the Republican response to dissuade them from plowing forward with the investigation, viewing the GOP attempts to raise process concerns as reflecting an inability to defend Trump’s conduct itself.

“The inquiry is because he has not honored his oath of office,” Pelosi told fellow Democrats on a private conference call Friday, according to notes taken by an aide on the call. “We will honor ours.”

Senate Republicans have struggled to answer the basic question of whether the crux of the impeachment allegation against Trump — asking a foreign leader for help to win an election — is acceptable conduct.

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Facing local media last week, GOP Sens. Joni Ernst of Iowa and Cory Gardner of Colorado — both up for reelection next year — dodged questions about whether Trump’s conduct was appropriate. Another Republican, Senate Foreign Relations Committee Chairman James E. Risch of Idaho, cut short an interview with a public-radio reporter in Boise rather than answer the question.

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Asked about the apparent momentum Democrats have built after a Trump rally in Louisiana on Friday, House Minority Whip Steve Scalise (R-La.) pivoted instead to process — attacking the probe led by House Intelligence Committee Chairman Adam B. Schiff (D-Calif.), a prime target of Trump and GOP attacks.

“He ought to know that if you run a kangaroo court, the people are going to look at it for what it is and know that he’s not taking it seriously,” he said of Schiff.

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Over the recess, the three committees charged with probing the Ukraine controversies had repeated success compelling witnesses to testify despite White House objections. Kurt Volker, the former special representative to Ukraine, gave the committees text messages depicting State Department officials coordinating with Trump lawyer Rudolph W. Giuliani to leverage a public promise of an investigation into the Bidens for a meeting between Trump and Ukraine’s new president.

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Former Ukraine ambassador Marie Yovanovitch — who unlike Volker is still a State Department employee — followed suit Friday, ignoring a State Department demand that she not testify, and Gordon Sondland, the sitting ambassador to the European Union, is expected to appear Thursday under subpoena.

“Increasingly, those who have served in the administration are unwilling to hide behind fallacious claims of privilege, unwilling to stand silent in the face of sequentially serious misconduct,” Schiff said in a recent interview. “In order for the president’s [stonewalling] strategy to work, he needs willing partners among those … in the administration, and not all of them are willing to go along with it.”

As the committees heard testimony last week, federal prosecutors in New York indicted two close Giuliani associates, Lev Parnas and Igor Fruman, who played a role in driving Trump’s interest in Ukraine by pushing theories about the country’s involvement in the 2016 election and the service of Biden’s son Hunter on the board of a Ukrainian energy company. The campaign-finance indictment from Trump’s own Justice Department has undercut Giuliani’s credibility and complicated White House attempts to promote a counternarrative focused on Biden’s alleged wrongdoing.

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An unpredictable factor is the fallout from Trump’s decision last week to withdraw a small number of U.S. troops from northern Syria, paving the way for a Turkish invasion of territory held by the Kurds, U.S. partners in the fight against the Islamic State. That move has prompted bipartisan outrage.

One Republican on the House Foreign Affairs Committee, Rep. Adam Kinzinger (R-Ill.), directly criticized Trump for his Syria pullout Monday in a tweet: “I thought you were going to defeat ISIS, that is why people voted for you. What changed? This is weakness. America is far more honorable than this.”

But neither Kinzinger nor any other Republican has moved to tie the Syrian pullout to the impeachment push, and one top GOP official went beyond that: Rep. Liz Cheney (R-Wyo.), the House Republican Conference chairwoman, said she was “very concerned” about Trump’s withdrawal decision in a Fox News Channel appearance Monday before suggesting that it was the Democratic impeachment push that set the stage for the Turkish invasion — not Trump’s decision to withdraw troops.

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“It was not an accident that the Turks chose this moment to roll across the border, and I think the Democrats have got to pay very careful attention to the damage that they’re doing with the impeachment proceedings,” she said, without citing evidence that the Turkish offensive was prompted by anything other than Turkey’s long-declared goal of clearing the Kurds from its border.

It’s not only Republicans who are averse to conflating the Syrian pullout with impeachment. Top Democrats are wary of muddying their case by expanding the impeachment probe beyond the bounds of the Ukraine allegations, a point Pelosi and others made on the caucus conference call Friday.

“There are a lot of rabbit holes to go down here, but we need to resist that temptation,” said one Democrat on the call who spoke on the condition of anonymity to describe a private call, paraphrasing Pelosi’s message. “Keep it clear in a way that is easy to communicate to folks.”

Meanwhile, the courts have given Democrats new reason to hope that they will ultimately be able to break the White House’s resistance to their oversight activities. Multiple federal judges ruled last week against the Trump administration on cases dealing with attempts to circumvent congressional oversight or otherwise short-circuit the legislative process. None was more crucial than a 2-to-1 D.C. Circuit decision upholding Congress’s right to inspect Trump’s business records, one that dismantled a White House argument that Congress had no “legitimate legislative purpose” to its oversight.

On Friday’s conference call, according to three people on the call, House Oversight and Reform Committee Chairman Elijah E. Cummings (D-Md.) tempered the victory, saying the ruling was likely headed to the Supreme Court, where there is a solid conservative majority that could overturn it. But rank-and-file Democrats said they were gratified to see even lower-court judges objecting to the White House’s noncooperation.

“That is the genius of our system, that no one house or branch holds all the power,” Crow said. “That’s the way that it is supposed to work.”

Correction: This story has been updated to correct Rep. Adam B. Schiff’s quote to “Increasingly, those who have served in the administration are unwilling to hide behind fallacious claims of privilege, unwilling to stand silent in the face of sequentially serious misconduct.” The original version said “salacious.”