WASHINGTON >> On Monday, it was a soft-spoken senior member of the Congressional Black Caucus, Rep. Emanuel Cleaver, D-Mo. On Tuesday, the careful chairman of the House Foreign Affairs Committee, Rep. Eliot L. Engel, D-N.Y., threw in his support. So did Reps. Jennifer Wexton and Jason Crow, two freshmen who flipped Republican seats in Virginia and Colorado.

On Wednesday, the influential chairwoman of the House Appropriations Committee, Rep. Nita M. Lowey, D-N.Y., added her voice.

The trickle of Democrats coming out in favor of opening a full impeachment inquiry is threatening to turn into a flood, raising pressure on Speaker Nancy Pelosi, D-Calif., to take the full House vote she has tried to avoid all year. This week alone, a dozen Democrats have announced their support for an inquiry, and with at least 116 declared supporters, the backers of an impeachment inquiry are more than halfway to the 218 votes they need in the House. They are two shy of a majority of the Democratic Caucus.

It was not necessarily supposed to go that way. The House’s departure Friday was expected to lower the temperature around the prospect of a formal impeachment inquiry against President Donald Trump. An unexpected declaration by the House Judiciary Committee in court papers Friday that an impeachment investigation was effectively already underway might well have cooled matters further.

But far from relieving pressure, the Judiciary Committee’s legal maneuver may have actually eased the way for more Democrats to come forward. Two high-ranking Democratic senators, Patty Murray of Washington and Debbie Stabenow of Michigan, also joined the fray this week.

“The president’s repeated abuses have brought American democracy to a perilous crossroads,” Engel said. “Following the guidance of the Constitution — which I have sworn to uphold — is the only way to achieve justice.”

For now, there are few signs that the rising support will translate into meaningful changes to the House Democratic leadership’s approach to an issue that deeply divides the country.

Pelosi and her top lieutenants remain skeptical of advancing a full-bore impeachment without broader public support and are steering the caucus forward with one foot tapping the brakes. They want to see if the House can use the courts to free up information and witnesses related to Robert Mueller’s investigation that are being blocked by the White House before reaching conclusions — a process that could take months, at best.

It appeared last week as if House leaders might have found a middle ground that could satisfy both proponents of an impeachment inquiry and queasy moderates still lined up against it.

On her way out of town last week, Pelosi blessed a proposal by the Judiciary Committee to take the position in court that the panel had already begun, on its own authority, “investigating whether to recommend articles of impeachment” against the president. Therefore, the panel said, Democrats did not actually need a House vote of the sort that was taken to initiate impeachment inquiries into Presidents Richard M. Nixon and Bill Clinton.

“The stance that she has taken is going to stay put for awhile,” said Rep. Mike Quigley, D-Ill., an advocate of an inquiry.

Democratic leaders always recognized that the August break could be an inflection point for some lawmakers, when conversations with their constituents could push them toward endorsing impeachment. But the drive toward an inquiry seems to be driven as much by internal politics on Capitol Hill as any push from voters. Impeachment was barely a whisper in two nights of Democratic presidential debate.

Quigley said individual members’ views are being shaped by a range of factors, including possible primary challenges, Mueller’s testimony last week, comments by Trump that are widely condemned as racist and the administration’s refusal to comply with certain investigative requests by Congress.

In June, Engel picked up a Democratic primary challenger, Jamaal Bowman, a middle school principal from New York City with the backing of Justice Democrats, the insurgent group that helped lift Rep. Alexandria Ocasio-Cortez, D-N.Y., to victory in her primary campaign against longtime Rep. Joseph Crowley.

A group of House Democrats from Washington state, along with Murray, made the jump in favor of an inquiry together Sunday, saying that they had waited to hear directly from Mueller and that their decision should come regardless of politics.

“Some suggest that the Senate is highly unlikely to convict the president should the House impeach him and that his chances of reelection will therefore be enhanced,” Rep. Denny Heck, D-Wash., said. “That may be true. What is truer is that nothing less than the rule of law is at stake.”

Cleaver framed his support for an inquiry around Mueller’s work, but in an interview with The Kansas City Star, he said he was also influenced by Trump’s racially charged attacks on his colleague Rep. Elijah Cummings, D-Md.

“If somebody dug deep into my psyche,” he said, “they’d probably dig out a nugget that it played a role.”

That might be what Pelosi once termed self-impeachment.

“It is hard to predict with this president what would trigger more movement,” Quigley said.

Republicans are watching in wait for what they believe could be a suicidal decision for Democrats. Trump has been eager to paint his opposition as ignoring the real needs of voters in favor of a blind pursuit of him — a frame he hopes to fix into place before his 2020 reelection fight. House Republicans have just as gleefully teed off on lawmakers, particularly moderates, who come out in support of an impeachment inquiry.

When Rep. Kim Schrier, D-Wash., who narrowly flipped a Republican seat in 2018, announced her support this week for an inquiry, the House Republican Conference’s campaign arm denounced her as a “deranged socialist” who was “so blinded by her hatred of President Trump that she is perpetuating impeachment conspiracy theories instead of working for her constituents.”

That campaign arm, the National Republican Congressional Committee, used similarly colorful language to tar Crow, who won a suburban district in Denver, and Wexton, who took a Northern Virginia seat. It is even going after vulnerable Democrats, like Rep. Abigail Spanberger of Virginia, who do not support voting to open an inquiry but have said the Judiciary Committee and others should stay their course.

That zealousness has some lawmakers concluding they might as well claim the credit from their liberal supporters and endorse an impeachment inquiry if they are going to take hits either way.

Crow, an Iraq War veteran, framed his decision as a continuation of his service to the country’s ideals.

But perhaps more important is pressure building on their left. There may yet be scant evidence that Mueller’s testimony before the Judiciary and Intelligence committees last week has meaningfully transformed public opinion, but it has given new fire to the resolve of pro-impeachment activists.

Need to Impeach, an advocacy group funded by billionaire presidential candidate Tom Steyer, spent six figures this week to run a 30-second ad highlighting Mueller’s testimony on CNN and MSNBC around the Democratic presidential primary debates to try to galvanize interest in the issue.

Today, along with three other left-leaning advocacy groups, it started a new campaign, “Impeachment August,” to mobilize voters to pressure their representatives.

The campaign’s website helps voters find town hall-style meetings in their districts and prods them to ask, “Will you uphold your oath to support and defend the Constitution and support an impeachment inquiry into crimes committed by Donald Trump?”

Their efforts could prove enough to persuade more reluctant lawmakers from safe Democratic districts who face little political cost in supporting an inquiry to come on board.

The pressure could be more awkward to navigate for moderates in seats that helped deliver Democrats the majority last year. When Rep. Andy Kim, who flipped his New Jersey district by less than 2 percentage points, faced voters in his district Tuesday night, he got an earful on the issue, the Burlington County Times reported.

“Why is it taking so long? I want him gone,” one attendee interjected. “Do your job” yelled another in reference to impeachment.

Kim stood his ground, explaining that he favored oversight investigations already happening in the House. But activists are looking to create many more similar moments.

“There is an opportunity right now for the Democrats to lead with clarity, and that’s going to help them,” said Ezra Levin, a founder of Indivisible, a grassroots network of progressive activists. “Looking weak and feckless does not help your reelection prospects; it’s going to hurt you.”