(CNN) President Donald Trump may have more room to fall in public attitudes toward his possible removal from office , detailed results from several new polls suggest.

While virtually every voter who approves of Trump's performance in office already opposes impeachment, there's still room for impeachment support to grow among voters who disapprove of how he's doing his job, according to detailed recent polling results provided to me from Quinnipiac and Monmouth universities.

In both polls, the share of such disapproving voters who consider Trump's interactions with Ukraine inappropriate still exceeds the share who back impeachment. That suggests that as more evidence emerges, or as Democrats present their final case, more of them may be persuaded that his interactions with Ukraine justify his removal.

The share of Trump disapprovers who support impeachment spiked from 66% to 87% just in the few days between Quinnipiac national surveys released on September 25 and September 30, according to results from the pollster.

This pattern of results signals that Trump's vituperative response to the threat of impeachment -- with his cries of "treason," " coup " and " civil war " -- may be energizing his supporters but is failing to persuade voters outside that core coalition. That's a familiar pattern from other issues in his presidency, from his advocacy of a border wall to his push to repeal the Affordable Care Act. In all those confrontations, Trump displayed very little capacity to move public opinion in general toward his position.

So to generate more opposition to his possible impeachment, the President faces a tough assignment: He must convert people who disapprove of his overall job performance or don't have an opinion about it.

Trump's framing of impeachment as a purely partisan assault on him and his voters has had one familiar effect: Very few Republican elected officials have felt politically safe enough to criticize any of his words or actions.

Republican pollster Gene Ulm says that's understandable: "I think the risks would be too high" for any Republican in Congress to break from Trump over impeachment, he says. "It's like death in a primary. You would be demolished."

Polling shows that, in most respects, Trump's offensive has succeeded in solidifying his base behind him. By 97% to 2% in the latest Monmouth Poll, and 98% to 1% in the latest Quinnipiac survey, virtually all voters who approve of Trump's job performance oppose impeaching and removing him from office, according to detailed results provided to me by both pollsters. Just 3% of voters who approve of Trump's job performance said they supported even an impeachment inquiry, Quinnipiac found. Only 2% of Trump supporters in the Quinnipiac Poll said the House inquiry is driven by concern about the facts, rather than political calculations.

But, as throughout his presidency, these voters who approve of Trump's job performance represent a clear minority of the electorate: 41% in both the Quinnipiac and Monmouth polls. In each survey, a much larger group of 53% disapproved of his performance. And in both surveys, those voters otherwise disenchanted with Trump's performance are converging around the extreme step of removing him from office.

Quinnipiac found that 87% of the voters who disapprove of Trump's performance in office already think he should be impeached and removed from office; in Monmouth the figure is a step behind, at 79%. In the Monmouth survey, 94% of those who disapprove of Trump's job performance say it was inappropriate for him to request that Ukraine investigate Biden. Among the voters who disapprove of Trump's overall job performance in the Quinnipiac Poll, 94% said he abuses the power of his office, 93% said he considers himself above the law, 89% said he did something wrong in Ukraine and 86% said he has committed crimes in office.

What will Democrats in Trump districts do?

These numbers could prove critical for the key block that will likely determine whether the House reaches 218 votes to impeach him: the 31 House Democrats holding districts that voted for him in 2016. (The 204 House Democrats holding districts that Hillary Clinton carried last time don't represent enough votes to generate a majority for impeachment on their own.)

Most of the Trump-district Democrats rejected the idea of impeaching him over his actions relating to Russia's interference in the 2016 election, and they initially moved cautiously toward considering impeachment in response to the whistleblower account about Ukraine . But while party insiders say many of them remain uncertain about how impeachment may play politically in their districts, most of them have moved toward the next step of supporting the inquiry.

The relatively broad public support for impeachment -- possibly magnified by unease over the tactics and threats Trump is using to resist it -- could make it easier for House Democrats in districts that voted for him in 2016 to take the next step and actually support impeachment. Some Democrats both on and off Capitol Hill believe that House Democrats in largely white-collar districts that voted for Trump will find it easier than their colleagues in mostly blue-collar Trump-leaning districts ultimately to support impeachment. The 31 Democratic-held Trump districts split almost exactly in half between those with more and fewer college graduates than the national average.

Jeff Link, an Iowa-based Democratic consultant, is one of many party strategists who think Trump's belligerent response will further erode his position in well-educated suburbs around the country, like those surrounding Des Moines.

"This rhetoric that he's been using even in the last week ... the sensible fiscal conservative, socially moderate Republican in Waukee and Ankeny and West Des Moines, they are probably repulsed by what he is doing," Link says.

While Trump's machine-gun accusations will get his evangelical and rural base "lathered up," Link adds, his harsh language could confirm the doubts about his personal behavior and temperament that led many white-collar suburban moderates to back Democratic House candidates last November.

"Trump helps them because it makes their criticisms of him more cogent," agrees Gary Jacobson, a University of California at San Diego political scientist. "His behavior makes it easier for them to oppose him in those kinds of districts. If it's suburban moms, he is doing exactly what alienates them in the first place."

'Different Republicans will react differently'

The latest surveys also highlight the possibility, albeit more remote, that more evidence could create some fractures in Trump's base. Although virtually no voters who approve of the President's job performance now support his removal, a measurable minority of them appear uneasy with the conduct that has triggered the impeachment inquiry.

In the latest Quinnipiac survey, only about 7 in 10 voters who approve of Trump said definitively that asking a foreign leader to investigate a political rival was not sufficient grounds for impeachment; the rest either thought it was (13%) or didn't know (16%). In the Monmouth poll, only 49% of Trump approvers said it was appropriate to make such a request of a foreign leader. Nearly another fourth said flatly that it was not appropriate and the rest said it depends or they didn't know.

The President's framing of the controversy as a partisan "coup" and "treason" meant to silence his voters could suppress those doubts among his backers. But longtime GOP strategist Bill Kristol, a leader among Republican Trump opponents, believes the President's characteristically bellicose approach is equally likely to widen divisions in the party, not only among voters but also elected officials.

"Different Republicans will react differently," Kristol predicts. "It might help him temporarily with House Republicans but endanger him over the medium term with Senate Republicans."

Kristol expects that almost all House Republicans will rally behind Trump's martial rhetoric. "The House Republicans are more Trump-y anyway," he says. "And they are a House minority, and fighting is what they do."

But, Kristol says, Trump's incendiary behavior might reinforce the doubts of some of the Senate Republicans who privately have expressed unease about his fitness for office. Most analysts generally think Trump faces the greatest risk of defection from the Senate Republicans facing swing state reelection campaigns in 2020, such as Cory Gardner in Colorado, Martha McSally in Arizona and Susan Collins in Maine. But Kristol believes older Senate "institutionalists" such as Tennessee's Lamar Alexander and Kansas' Pat Roberts -- both of whom plan to leave office when their terms end after next year -- may be more likely to break ranks.

"They must look at this and say, 'Holy cow, this is crazy,' " Kristol says. "Is any one of them going to be the first one to jump and say, 'I'm going to convict'? People who aren't up for reelection, who are more sober and serious, they could all say we cannot go down this path."

Still, the precedent from Watergate suggests that if Senate Republicans break from Trump on impeachment they will be far more likely to be leading than responding to opinion in their party. During most of the Watergate investigation, only about one-fifth of Republican partisans supported removing President Richard Nixon from office in Gallup Polling, notes Jacobson. Even in the final Gallup Poll before Nixon's resignation, nearly three-fifths of Republican partisans said he should not be removed.

Yet senior GOP Senate leaders defied that current to tell Nixon that his support there had crumbled, an appraisal that helped trigger his resignation. The next few months will measure how many, if any, officials from this generation of Republican senators will follow that path.