In the abstract, the views of American voters about impeachment don’t really matter. House Democrats launched an inquiry in late September to address questions about President Trump’s interactions with Ukraine. That inquiry may result in articles of impeachment, on which the House can then vote. If any pass, the Senate will then hold a trial for the president and decide whether his actions warrant his removal. In other words, it’s up to 435 members of the House and 100 members of the Senate to judge what Trump did, not for Americans to do so.

That is not how it works, though, for a number of reasons. For Democrats, impeaching Trump is also a rebuke of his leadership. Potentially removing him from office offers its own appeal. More obviously, those 535 elected officials represent their constituents, and if the constituents support impeachment or reject removing Trump from office, that’s an important guideline for the elected officials. For both parties, taking votes in opposition to the views of their constituents poses a career risk, one that elected officials are generally wary of taking.

So all eyes are on how views of impeachment are shifting. Are the open hearings being held by the House changing perceptions of impeachment? Is support for removing Trump from office growing?

New polling suggests that the shifts so far have been modest. Importantly, it also suggests that most Americans are intractable on the subject and that the group most likely to be persuaded is independents — making it unlikely that many Republicans representing solid-Republican districts would join votes condemning the president.

There has been a slight uptick in support for impeaching Trump and removing him from office since the public hearings began. Data aggregated by FiveThirtyEight shows that a seven-day average of polling on the question of removal has risen non-significantly since the open hearings began. The rise in support after the inquiry was announced, by comparison, was much sharper and significant.

What’s intriguing are the shifts by party. Small increases among Democrats and independents — and a downturn among Republicans. Generally speaking, there hasn’t been a significant change in views since the inquiry began. If these are the starts of trends among party groups, though, it suggests an uphill climb for persuading members of Trump’s party.

That shift among independents is intriguing, though, particularly when coupled with a new NPR-PBS NewsHour-Marist poll considering views of impeachment.

Asked whether they might change their minds about their position on impeachment, most respondents — nearly two-thirds — said they wouldn’t. Those who say they’re paying very close or fairly close attention to the impeachment developments were slightly more likely to say they might change their minds than were those paying not too much or no attention.

But note the difference by party. Nearly 2 in 5 independents say their minds might be changed, compared with about a quarter of Democrats and Republicans.

Another survey, conducted by ABC News and Ipsos, shows that independents were the most likely to say that their minds were changed after the first week of public hearings. A plurality of Democrats had mostly made up their minds on impeachment before any of the Ukraine news broke.

About half of those who made up their minds in the past week were independents, according to the ABC-Ipsos survey. Of the 21 percent of respondents who said they had decided on impeachment in that time frame, 6 in 10 supported impeaching and removing Trump.

That said, the NPR-Marist poll still shows that most independents aren’t likely to change their minds. In another question, independents were evenly split on whether new testimony made them more or less likely to back impeachment. Those who were paying close attention said they were more likely to support impeachment, though that, to some degree, reflects that Democrats are more likely to say they are paying close attention.

That holds for views of impeachment in general, too, with close watchers of impeachment more likely to support Trump’s ouster. It’s worth noting that independents in the NPR-Marist poll were less likely than respondents overall to support impeachment. (Interestingly, not many people held an impeach-but-don’t-remove position.)

One reason that minds might be unlikely to change is that most respondents already have strong views of the impeachment inquiry. Six in 10 people overall already have a strong view of the inquiry, as do two-thirds of Democrats and nearly three-quarters of Republicans. The partisan group least likely to have a strong view of the inquiry was independents — though more than half still did.

Those not paying much attention to the impeachment were least likely to have a strong view.

Interestingly, there’s not much difference between those watching the impeachment closely and those who aren’t on issues that are central to what’s being discussed. For example, most respondents, including most of those who are and aren’t closely watching the inquiry, think that asking a foreign power to investigate a political opponent is not acceptable. (A plurality of Republicans think that it is acceptable.)

Most respondents, independent of how closely they’re watching the impeachment probe, also think that the identity of the intelligence community whistleblower who helped bring attention to the Ukraine issue should be protected.

What elected officials will be paying the most attention to, however, is probably this finding from the NPR-Marist poll. Respondents were more likely to say that a vote in support of impeachment from their representative would make them less likely to support that representative next year. More than half of Republicans said they would be less likely to support that representative.

Significantly, about half of those opposed to impeachment said they would be less likely to back a representative voting for impeachment. Only about a third of those supporting impeachment said it would make them more likely to vote for such a representative.

This is the data that elected officials will be watching most closely over the coming weeks, on the off chance that the numbers move. In the abstract, this poll result shouldn’t affect how members of Congress vote. In reality, it will no doubt be a significant factor.