“It is one act after another of obstruction of justice by the White House, by the State Department, and by the attorney general. And I say, give them more rope to hang themselves,” Rep. Harley Rouda (D-Calif.), who flipped his conservative Orange County district in 2018, said in an interview.

Yet some Democratic lawmakers and aides have begun to say privately — and, to a lesser extent, publicly — that the House should just vote to formalize the inquiry, robbing the GOP of its main talking point.

The debate is threatening to cleave Democrats’ unified front as the White House makes the arcane procedural arguments the centerpiece of its impeachment defense.

“If Nancy asked me, I would say sure, let’s have a vote. Everybody’s on record, so they’re not going to vote any differently. What’s the danger in having a vote to formalize it?” said Rep. John Yarmuth (D-Ky.), an early impeachment backer.

But the suggestion has provoked strong objections from some of their colleagues who say they would be abdicating their authority if lawmakers permit other branches of government to dictate their procedures.

“If we allow that to happen, Congress would be completely dysfunctional,” Rep. Sean Casten (D-Ill.) said at a recent town hall event in Glen Ellyn, Ill. “If we have to take a complete show vote, we'll get the vote. But I find it offensive that they are basically telling us how to do our job with a misreading of the Constitution. Read the freakin’ Constitution. And then let’s honor our oath to it.”

In a letter to Pelosi earlier this week, White House counsel Pat Cipollone said the House was undertaking a “constitutionally invalid” and “illegitimate” impeachment process that absolves lawmakers of “taking political accountability.” The strategy is focused more on the process Democrats have undertaken, and less on defending Trump from allegations that he abused his power by pressuring Ukrainian President Volodymyr Zelensky to investigate Joe Biden and his son, which is the chief focus of Democrats’ impeachment inquiry.

Though a small but growing chorus of Democrats has started urging a vote simply to undercut this GOP talking point, others say that nothing will stop Trump and his supporters from claiming Democrats’ efforts are unfair and inconsistent with past impeachment procedures. They say the party shouldn’t take the White House’s bait, arguing that the president’s defenders will simply find other reasons to not comply with the inquiry.

“The debate on our side about whether we should or shouldn’t is kind of academic because no matter what we do, the president won’t cooperate,” Rep. Peter Welch (D-Vt.), a member of the Intelligence and Oversight committees, said in an interview.

Though the debate is largely happening in private, it flared up publicly this week when one of Pelosi’s California allies urged her to call a formal vote, arguing that Cipollone’s letter effectively shut the door on cooperating with House Democrats.

“They want a fight? OK, let’s arm ourselves completely and totally with the full power of Congress,” Rep. John Garamendi (D-Calif.) said Wednesday on CNN. “I do think that it’s time for us to put a vote on the floor — a resolution for the inquiry structured in such a way that it can move forward with full power of the Congress behind it.”

But embracing those arguments would represent a reversal for House leaders.

Democrats have long argued that they don’t need a vote to launch formal impeachment proceedings, even if that had been the practice in prior presidential impeachment processes. In fact, House lawyers backed by Pelosi have made that argument in a succession of court cases seeking evidence to support their impeachment inquiry, and proponents of that position worry a formal vote would undercut their legal claims.

Similarly, Democrats are worried that a near-term floor vote would drive away a handful of Republicans who are wavering over whether to support impeachment proceedings. A party-line vote would hand the White House another talking point, they argue: that impeachment is a purely partisan effort by Democrats.

But Pelosi may have more than simply GOP talking points on her mind.

The House is fighting in court to access former special counsel Robert Mueller’s closely guarded evidence, and House lawyers say they need it to support their ongoing impeachment inquiry. The Justice Department rejected this argument, contending that the House’s claim to be in the midst of an impeachment process is invalid because there has been no House vote to authorize it.

Though the case is unrelated to the Ukraine scandal now at the center of House Democrats’ impeachment inquiry, it could determine whether Pelosi changes course and holds a vote on opening an inquiry.

Earlier this week, the judge in the case — Beryl Howell, the chief judge of the U.S. District Court in Washington — indicated she was inclined to support the House’s position. But she added that a vote would “make my life very much easier.” Republicans have said a formal vote is the only way for a judge to recognize that an impeachment proceeding has begun.

“Without an explicit authorization from the full House, the Court has no determinative measure of when an official impeachment proceeding has begun and when the Committee is merely exercising its normal oversight powers,” Georgia Rep. Doug Collins, the top Republican on the House Judiciary Committee, wrote in a recent filing in the case.

“Votes — not words or press conferences by Members, the Chairman, or the Speaker — are the mechanism through which Congress acts,” Collins added.

But Howell appeared more amenable to Pelosi’s view — that nothing in the Constitution or in the House’s rules require a formal vote. Howell is expected to rule in the case later this month.

In the past, when judges have suggested the House should take a vote, Pelosi has responded by doing just that, taking action to preempt unfavorable rulings in court.

Earlier this year, Neomi Rao, a Trump-appointed federal appeals court judge, suggested that a full House vote would be necessary in order to buttress the House Oversight Committee’s subpoena seeking Trump’s financial records. Almost immediately, the House passed a largely symbolic resolution that puts the weight of the full House behind their subpoenas.

Many lawmakers, though, have criticized the idea that the House’s procedures must be dictated by federal judges. Democrats have long maintained that a vote to authorize an impeachment inquiry is unnecessary, but Republicans have pointed to the Clinton and Nixon impeachment processes as precedents for a full House vote.

“It’s a distinction without a difference, and I don’t think we have to pander to the demands of the Department of Justice,” Rep. Gerry Connolly (D-Va.), a senior member of the Oversight panel, said in an interview.

Pelosi has long tried to protect her most vulnerable members from politically difficult impeachment-related votes. This vote in particular would give Republicans another opportunity to slam those Democrats whose districts have been historically difficult for the party to compete in. But one of those vulnerable lawmakers, Rep. Elissa Slotkin (D-Mich.), indicated she would support Pelosi’s decision if she moved to hold a vote.

“I don’t think a vote is a hard thing to do. I think it’s a delay tactic. But if they need to have it, I’m not against it,” Slotkin said on CNN Wednesday night.

But Rouda, who, like Slotkin, is vulnerable in 2020, believes Republicans would face more political risks than Democrats with a vote on opening a formal impeachment inquiry.

“When that vote comes to the floor, Republicans in swing districts are going to have to make a decision as to whether to continually provide blind faith to the president, blind loyalty to the president, or uphold the oath they took to defend the Constitution of the United States of America,” he said. “And everybody in the United States is going to see exactly where they stand.”

Sarah Ferris contributed to this report.