(CNN) Vulnerable House Democrats privately met with Speaker Nancy Pelosi on Thursday to air out their views about the impeachment process, including some still resistant to the notion of impeaching President Donald Trump.

During the meeting, several members made clear their stance that Democrats should keep the inquiry focused on the Ukraine matter -- allegations that Trump asked the Ukrainian President to initiate an investigation into a potential 2020 political rival -- and not the other instances of potential wrongdoing detailed in the report from special counsel Robert Mueller

Democrats are largely in agreement about the strategy, with Pelosi saying during her press conference on Thursday morning that the whistleblower complaint is "the focus of the moment."

By keeping the impeachment inquiry focused, leaders hope to keep the caucus unified -- with an eye to the moderate members who only recently joined calls for proceedings. The Ukraine matter is also relatively clear-cut and easy to explain to the public, lawmakers say. They also argue the probe, spearheaded by the intelligence committee, will be able to move faster -- possibly in the next month or two -- with a narrower scope.

Rep. Angie Craig, a vulnerable freshman Democrat from Minnesota, who said earlier this week that she supported the impeachment inquiry said after the meeting that Pelosi and Democratic leaders mostly listened to the views raised by the lawmakers.

"I'm in a district where I've been reluctant to move forward only from the perspective where I want to be disciplined, I want to look at due process and want to make sure we get all of our facts -- and this process will allow us to do that," Craig said, adding she backed a narrow probe led by the House Intelligence Committee

Rep. Matt Cartwright, a Democrat from Pennsylvania, told CNN that he wouldn't -- at this point -- vote for articles of impeachment

"I would vote no right now because we haven't seen all the facts," Cartwright said. "We have to presume that people are innocent, don't we, and we have to see if what the press has been reporting and what has been revealed in terms of documentation, if if all that is true."

Democrats will hear from constituents about their moves toward impeachment soon, with members scheduled to return to their districts for a two-week recess at the start of October. It will be the first time a swath of members from more conservative districts will receive clear, in-person feedback -- or, in some cases, blowback -- from the people they represent since they joined calls for impeachment proceedings in the wake of the Ukraine allegations earlier this week.

But Rep. Dan Kildee, a Michigan Democrat, said the timing of the recess has its upsides.

"I really can't think of a better thing to do than to sort of check in with the boss before we move forward," he told reporters. "It's actually good timing that we get a chance to go home, catch our breath, get the perspective of people back home, explain what we're doing, and then come back and move forward accordingly."

Once lawmakers return, though, movement is likely to be quick.

"I think it's everybody's intention here to get this done in 2019," said Rep. Jamie Raskin, an impeachment advocate and member of the Judiciary Committee.

"The caucus is unified around the lawlessness and corruption pouring forth from the White House, and our job will be to reduce it to a set of articles of impeachment that make sense to the country," the Maryland Democrat told reporters on Thursday night. "We need a set of articles that make a compelling legal case and that tell a coherent story to the public. And if we do our job right, it will be a unifying exercise for the whole country."

Rep. Anthony Brindisi, a freshman from New York who has resisted calls for an impeachment probe, told CNN that he's "not yet" there on impeaching Trump.

"While I find many of the statements in the whistleblower's report disturbing, there's a lot more information that's out there," Brindisi said. "We have to talk to some of these officials that they have listed in the report here and see where it goes."

More than half the members of the US House of Representatives have said they support an impeachment inquiry, according to a CNN count . However, that count includes many Democrats who say they support an impeachment investigation but are still waiting for the results of the probe before deciding whether to finally vote to impeach Trump. Even if the House could pass the vote, it likely would go nowhere in the Republican-controlled Senate, one of many reasons the issue has been politically divisive in the party.

Still there has been a surge in support -- more than 75 House members in about three days -- of launching such an inquiry as part of the fallout from Trump's July 25 call with Ukrainian President Volodymyr Zelensky where he discussed former Vice President Joe Biden. There is no evidence of wrongdoing by Biden.