(CNN) Nancy Pelosi has made clear -- over and over again -- that she opposes the Democratic-controlled House trying to impeach President Donald Trump right now.

"I'm not for impeachment," she told The Washington Post in March. "Impeachment is so divisive to the country that unless there's something so compelling and overwhelming and bipartisan, I don't think we should go down that path, because it divides the country. And he's just not worth it."

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And, Pelosi has, for the most part, been able to enforce that position among her House Democratic colleagues over the intervening few months -- even as special counsel Robert Mueller's report was released and showed multiple occasions in which Trump seemed to commit obstructive behavior in regard to the special counsel probe looking into Russian interference in the 2016 election.

"House Judiciary Chairman Jerry Nadler discussed with Pelosi the advantages of an impeachment inquiry in terms of adding weight to a court case, according to a source with direct knowledge. Nadler, whose committee has been on the front lines of investigating the findings from within special counsel Robert Mueller's report, broached the topic with Pelosi because several members of his committee have been pressing to open an inquiry ...

... The tensions displayed behind closed doors underscore the growing divide within the caucus about how to proceed in the face of White House resistance to all its demands, as Pelosi and some of her top confidants argue that acting with too much haste would be a gift to their political foes while a growing faction of Democrats -- that now includes several high-profile and high-ranking members -- push them to take a tougher stand against what they call a lawless President."

To be clear: This isn't an open rebellion just yet. And that is a testament to the power and fear that Pelosi retains among Democrats in the House. Because, under any other leader, the floodgates on impeachment would have already burst open.

The political problem Pelosi is trying to navigate is a decidedly thorny one -- made even more complicated by the Trump White House's total refusal to cooperate in any way with the ongoing investigations being led by House Democrats.

On the one hand, Pelosi knows that many within her caucus believe that Trump has already done enough -- according to the Mueller report -- to be brought up on impeachment charges. And that there are those, like Nadler, who view the House playing the impeachment card as part of a broader attempt to bolster and backstop the broader legal fight between Congress and the executive branch over what the former is entitled to and the latter is required to provide. (The legislative branch won a major victory -- albeit an early one -- in that fight on Monday.)

Plus, the base of the party favors such a move -- 69% of self-identified Democrats said so in a May CNN poll -- although they are less unified in support of impeaching Trump than they were last year, when 80% favored impeachment in a December CNN survey

"I believe we have come to a time of impeachment," influential New York freshman Rep. Alexandria Ocasio-Cortez said Tuesday. "I think that at a certain point, this is no longer about politics, but it's about upholding the rule of law."

On the other hand, Pelosi knows that even if the House were to impeach Trump, it would die in the Republican-controlled Senate, where there are no signs that support for the President is cracking. If anything, support for Trump among Republican senators has grown strong since the release of the Mueller report.

To pursue impeachment in the House given its near-certain death in the Senate, then, would be to charge at a bit of a political windmill. (Many Democratic base voters know this and want the party's leaders to do it anyway solely because of the principle of the thing.)

And, there is reason -- polling, to be specific -- that suggests this doomed attempt at impeachment could have major -- and negative -- political repercussions for Democrats. In the May CNN poll , just 37% of American want Trump impeached while 59% disagreed with such a course of action. That same poll showed that 44% say Democrats are going too far in investigating the president -- an increase from 38% saying so in March. (One in 4 voters said Democrats in Congress were doing too little to investigate Trump; while 28% said they were doing about the right amount.)

This is a classic rock-and-a-hard-place choice for Pelosi. While her let's-wait-and-see approach has sated the base -- and many members of her caucus -- until now, with every passing day that the Trump administration stonewalls legislative attempts at oversight, her position becomes that much harder to hold. And, if Democrats were to lose a major legal fight in the coming weeks over their demands for more information and transparency from the Trump administration, it's hard to see how Pelosi holds back the forces pushing for impeachment -- no matter the potential political impacts on the party come 2020.

What's clear from the last 24 hours of closed-door meeting among House Democrats is that patience is wearing thin for Pelosi's slow-walk approach on impeachment. There's an itch for action -- and Pelosi may not be able to keep her colleagues from scratching it much longer.