The House’s impeachment inquiry is moving from secure conference rooms underneath the Capitol and into the public eye. On Wednesday, diplomats William Taylor and George Kent will testify in open hearings, followed by former U.S. ambassador to Ukraine Marie Yovanovitch on Friday. And as House Democrats begin to present the evidence they’ve gathered in a series of televised hearings, they face the difficult task of persuading a deeply divided country that President Trump’s pressure campaign on Ukraine amounts to an impeachable offense.

According to FiveThirtyEight’s impeachment polling tracker, Americans are narrowly split on whether Trump should be impeached and removed from office — as of publication, 47.2 percent are in favor and 45.0 percent are against. (Support for beginning the impeachment process is a little higher, at 51 percent.)

As you can see in the chart above, Democrats seem to have already picked off most of the persuadable voters when it comes to impeachment support, too. The share of Americans who think Trump should be impeached and removed has been essentially unchanged since mid-October. So how much can the Democrats’ public hearings be reasonably expected to shift the needle?

In the past, congressional hearings have been a powerful weapon. When control of the government is divided between two parties, investigations have been a vehicle for the House majority to publicly and repeatedly hammer the president. And research has found that the cumulative toll of hearings has been effective in weakening presidents, particularly as it pertains to their approval rating, so a blitz of hearings outlining the case against Trump could harm him. But then again, Trump has proven surprisingly resilient in the face of House Democrats’ investigations so far — although his approval rating is hovering around its lower bound at 41.3 percent, it hasn’t yet dipped below 40 percent, according to FiveThirtyEight’s tracker of presidential approval. There’s reason to believe that could continue even after the impeachment process goes public.

Congressional investigations can hurt presidents’ approval ratings — but not always

In the past, the relentless negative attention generated by hearings and investigations was a fairly effective way to undermine the president — or at least that’s what political scientists Eric Schickler and Douglas Kriner have found in their analysis of data on congressional hearings held between 1953 and 2014. In their book on congressional investigations, they found that when the party controlling the House was not the president’s party, there were on average 37 more investigative days, and those hearings systematically lowered presidential approval ratings.

And when Kriner and Schickler modeled the relationship between presidential approval ratings and investigative activity, they found that more days of hearings dragged down a president’s approval rating. For instance, a month with 20 days of investigative hearings caused an approximately 2.5-percentage point drop in presidential approval; for a month with 40 investigative hearing days, presidential approval fell by around 4 points. (This was after even controlling for external factors that may affect views of the president, like the state of the economy. They also accounted for the effect that presidential approval can have on Congress’s willingness to investigate to begin with.)

The lesson here for Democrats is that investigations that unfold over weeks or months, rather than days, have historically damaged the president. Kriner and Schickler didn’t try to isolate the specific impact of hearings related to impeachment (although they were included in the dataset), but in an interview, they pointed out that President Nixon’s approval rating fell significantly in the summer of 1973, when the Senate Watergate Committee held weeks of public hearings on Nixon’s ties to the Watergate burglary and cover-up, which 71 percent of Americans watched live.

But the impeachment process is especially complex, and it hasn’t always negatively impacted the president. President Clinton’s approval rating remained high throughout his impeachment, never dipping below 60 percent. House Republicans only held four hearings during the entire process, though, so it’s hard to say what would have happened if they had conducted a longer, independent investigation.

Previous public hearings haven’t appeared to weaken Trump

Of course, this isn’t the first investigation of Trump House Democrats have launched. Democrats reopened the House investigation of Russian interference into the 2016 election soon after taking control of the chamber, and in connection with this and other investigations of the president, secured high-profile, public testimony from former Trump lawyer Michael Cohen and special counsel Robert Mueller — yet neither appeared to substantially change opinions of Trump or of impeachment. So it’s entirely possible that the public impeachment hearings won’t have a big effect on either support for impeachment or Trump’s approval ratings.

One theory for why Trump’s approval ratings might be unusually resilient in the face of investigations is that it’s already quite low and is also incredibly steady. Past presidents’ favorability has tended to fluctuate in response to news events, but starting with President Obama, voters’ views about the president’s job performance have been much less variable. “We may be in a world where there’s a core of Americans who will continue to support the president no matter what’s revealed about him,” Schickler said.

And Democrats’ time crunch could limit the impact as well. They’ve already scheduled three hearings, but it’s unclear how many more days of open testimony they’ll be able to get on the calendar before public phase wraps up.

The impeachment hearings could have a bigger impact, but it will still be an uphill climb

One big difference between the upcoming impeachment hearings and Democrats’ previous investigations of Trump is the number of people who are willing to testify publicly. Before the Ukraine allegations broke, Democrats struggled to secure testimony from people who could shed light on what was happening in the Trump administration. And although the Trump administration has refused to cooperate with the impeachment inquiry, a number of bureaucrats and diplomats have appeared for closed-door depositions anyway, and will now be testifying publicly. The televised hearings will likely unfold over several weeks and will be closely covered by the media, which are both promising signs for Democrats. “The cumulative weight of the hearings and the coverage is exactly the kind of thing that can lead to approval ratings being dragged down,” Schickler said.

But that doesn’t mean that the hearings will lead to a huge shift in people’s views. Kriner said it might be easier to nudge people in favor of impeachment than to erode Trump’s approval ratings, since disapproval of Trump currently appears more entrenched than support for impeachment. But the fact that some of the biggest bombshells to come out of the investigation are already public — like European Union ambassador Gordon Sondland’s recent confirmation that military aid to Ukraine was contingent on the country announcing a probe of the Bidens — might dampen the effect of the hearings. It could potentially even result in a situation similar to the Russia investigation, where many of the most dramatic details in Mueller’s final report were already made public through court documents and reporting.

“There are advantages to having dramatic moments where unexpected things are said,” Kriner said. But because a lot of the facts are already known, he added, a big swing in opinion seemed unlikely: “[F]rankly it’s just very hard to know what would change the minds of the people who are still on Trump’s side.”