Washington (CNN) There's a reason House Democrats haven't started impeachment proceedings against President Donald Trump yet: almost none of their most vulnerable members support the move.

CNN reached out to 41 freshmen Democrats who flipped Republican seats last year to ask if they currently support starting an impeachment inquiry. The results were telling -- nearly half (20) didn't respond. Of those who did, the vast majority were either a "no" or undecided.

Known as the "majority makers" or "front-liners," this group was key to securing the Democrats' House majority last year. And Democratic leaders are intensely focused on holding those districts in 2020.

That gives these members enormous influence in whatever direction the party takes -- and hardly any are calling for impeachment.

Of the 43 Democratic challengers who flipped seats from red to blue in 2018, only two -- Reps. Tom Malinowski of New Jersey and Mary Gay Scanlon of Pennsylvania -- have publicly said they support opening an impeachment inquiry. And only Scanlon represents a more liberal seat than her Republican predecessor due to redistricting.

What we asked

CNN asked the remaining 41 members where they stand on opening an inquiry. Of the 21 that responded, it was clear that most of them aren't on board with an impeachment push -- though many aren't entirely ruling it out.

Ten offices told CNN that they did not support an inquiry at this time, and by CNN's count, 11 were undecided.

Many who did respond issued statements urging the House to push forward with the various investigations into Trump's campaign, administration and finances , suggesting that they could be open to starting an impeachment inquiry at a later point even if they are not calling for it now.

In what could be a tough vote for some Democrats who just want to move on from the issue, the House votes Tuesday on a resolution to authorize court action to enforce subpoenas for Attorney General William Barr and former White House counsel Don McGahn.

The House will also vote to empower committees to bypass full floor votes for civil contempt actions to go to court with their subpoenas -- a move that could take some pressure off these Democrats from Republican districts.

Even if Democrats in swing districts ultimately decide to support an impeachment inquiry, that doesn't mean it will happen. House Speaker Nancy Pelosi has made it clear she wants bipartisan support for an impeachment path before she pursues one, and so far only one Republican has called for an inquiry , Rep. Justin Amash of Michigan.

If the 60 or so House Democrats who currently support an inquiry are to succeed, they'll need to convince their moderate colleagues first. That will be difficult, since these Democrats face a complex political calculation on the issue.

"Nobody knows what the political impact will be, and therefore it is a risk," Malinowski told the New Jersey Star-Ledger in late May, describing his decision to support an impeachment inquiry

As long as Malinowski remains an outlier among moderate Democrats, Pelosi is likely to continue resisting calls for impeachment from the left flank of her caucus, urging House committees to continue their investigations of Trump instead.

Regardless of her political strategy, Pelosi made her personal feelings known last week, when behind closed doors she told Democratic leaders she wanted to see Trump in "prison," according to Politico.

Keep investigating

Most of these moderate Democrats have made clear that they want to see the current investigations in Congress proceed and see where that leads.

"I'm very deliberate and thorough, and I don't want to go down any road until I have all the facts," Rep. Jennifer Wexton of Virginia, said at a recent town hall when asked about impeachment. "So all options are on the table."

The office of Rep. Donna Shalala of Florida told CNN that the congresswoman "is undecided until the Judiciary Committee completes its work," a reference to current and ongoing investigations.

Shalala recently told the Sun-Sentinel newspaper that she is not ready to support an inquiry at this time, but indicated that could change. "Not yet, but you know, we're getting closer and closer," she said.

In their statements to CNN, some members underscored the gravity of impeachment and how an inquiry is not to be taken lightly.

"Going down the path of impeachment would be very divisive for the country," Rep. Elaine Luria of Virginia told CNN in a statement. "We need to have all of the facts before we consider such an option, and I support the important investigative work being done by the appropriate committees in the House."

No way

Other members in swing districts are flat out opposed to impeachment, and say it's simply time to move on.

"I'm not in favor of impeachment. I think we've got to move forward and try to look at issues that we can find compromise on," Rep. Anthony Brindisi of New York told New York Now in late May, adding, "This is what I'm hearing from people back home who are not focused on that issue, but are focused on the immediate concerns that they are facing."

Rep. Jeff Van Drew of New Jersey said he's practically "done" with talking about impeachment and that people are "tired of the investigations."

"I welcome conversations on improving the lives of Americans, on immigration, on health care, on any of the many issues that affect people every day," he said. "But what I am done with, barring any new evidence, is any talk of impeachment, investigations, or divisive, unproductive politics."

Undecided

In between are some members who are openly undecided on which way they're leaning. At a town hall recently, Rep. Katie Porter of California said she had seen "a real turning point" on the impeachment push, but "I haven't made a public decision yet."

And some, like Rep. Mike Levin of California, are open to the possibility of an inquiry, but still are not calling for one themselves at this time.

In a statement to CNN, the congressman explained that he plans to defer to the judgment of his colleagues on the House Judiciary Committee and "if they deem it necessary" to start an inquiry, he would support that.

"I do not sit on the House Judiciary Committee, but I trust the judgment of my colleagues who do. If they deem it necessary to begin an impeachment inquiry as the most effective means to proceed, I will support that decision," he said.