Democrats face the challenge of keeping the heat on President Trump Donald John TrumpBiden says voters should choose who nominates Supreme Court justice Trump, Biden will not shake hands at first debate due to COVID-19 Pelosi: Trump Supreme Court pick 'threatens' Affordable Care Act MORE with several more weeks of the impeachment process left to play out.

Trump’s opponents have showcased some deeply damaging evidence against the president in recent weeks. Public support for impeachment over the president’s dealings with Ukraine has reached levels that were never matched during former special counsel Robert Mueller Robert (Bob) MuellerCNN's Toobin warns McCabe is in 'perilous condition' with emboldened Trump CNN anchor rips Trump over Stone while evoking Clinton-Lynch tarmac meeting The Hill's 12:30 Report: New Hampshire fallout MORE’s investigation into allegations of Russian collusion.

But most of the Ukraine testimony is now in the rearview mirror. And while impeachment itself scores relatively well in opinion polls, Trump’s approval rating has barely budged, even since the House inquiry began in late September.

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In the rolling job approval average calculated by data site FiveThirtyEight, Trump has hovered between 40 percent and 43 percent approval, and 52 percent to 55 percent disapproval, for almost 10 months.

The president and his allies are hitting the impeachment inquiry every day, lampooning leading Democrats like Speaker Nancy Pelosi Nancy PelosiPelosi: Trump Supreme Court pick 'threatens' Affordable Care Act Sunday shows preview: Lawmakers prepare for SCOTUS confirmation hearings before election Will Democrats attempt to pack the Supreme Court again? MORE (Calif.), House Intelligence Committee Chairman Adam Schiff Adam Bennett SchiffSchiff to subpoena top DHS official, alleges whistleblower deposition is being stonewalled Schiff claims DHS is blocking whistleblower's access to records before testimony GOP lawmakers distance themselves from Trump comments on transfer of power MORE (Calif.) and House Judiciary Committee Chairman Jerrold Nadler Jerrold (Jerry) Lewis NadlerDemocrats shoot down talk of expanding Supreme Court Schumer: 'Nothing is off the table' if GOP moves forward with Ginsburg replacement Top Democrats call for DOJ watchdog to probe Barr over possible 2020 election influence MORE (N.Y.).

The danger for Democrats is that the public is beginning to tune out the impeachment process.

There is also a lack of basic suspense, given the rare degree of consensus as to how the process is likely to end: with impeachment by the Democratic-majority House and acquittal by the Republican-majority Senate.

That could pose problems for Democrats who want even moderate voters to feel — and keep feeling — maximum outrage about the president’s actions.

Some Trump loyalists, meanwhile, are expressing relief with the sense that the worst may be over for the president, at least once impeachment charges are formally filed.

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“The fact is that the indictment should be the worst that the president will see, because when it moves to the Senate it is going to be a totally different animal,” said Brad Blakeman, a veteran of former President George W. Bush’s White House and a strong Trump supporter.

Blakeman insisted that, politically speaking, Trump had stood up to the charges laid against him “quite well.”

“I don’t see the fortunes being reversed when you get to the trial,” he added.

Still, it’s hardly as if Trump is out of the woods.

His approval ratings may be consistent — but they are very weak by historical standards.

His standing with female voters, in particular, is a huge handicap going into 2020. In the latest Economist-YouGov poll, conducted last week, he won the approval of only 38 percent of women, while his job performance was given the thumbs-down by 53 percent.

So far, there hasn’t been much sign that impeachment itself is proving to be a loser for Democrats nationwide, as some skeptics had at one point suggested.

The Economist poll showed a plurality of Americans backing both Trump’s impeachment (45 percent to 39 percent) and his removal from office (47 percent to 40 percent). Even independent voters in the poll backed Trump’s ouster, albeit by a thinner margin of 40 percent to 37 percent.

A Reuters-IPSOS poll conducted during the same period also found a plurality in favor of impeachment, 44 percent to 42 percent. Independent registered voters favored impeachment by a slightly wider margin in that survey, 45 percent to 39 percent.

Virtually everyone acknowledges that huge swings in public opinion are off the table in the current hyperpolarized environment. Democrats say the yardstick by which they should be judged, politically, is whether they can keep the poll numbers around where they are now.

To do so, said Democratic consultant Bill Carrick, they should use the hearings to “keep it off the politics of the moment and more into the facts and the details. That’s the best case they have to make, and that requires the discipline to ignore the guerrilla tactics of the Republicans.”

Carrick was alluding to some of the angrier Republican interventions during hearings, an approach that was seen again in a quarrelsome session of the House Judiciary Committee on Monday.

Carrick acknowledged that Trump has “a pretty good hold” on his own base and that, if others in the Democratic Party were hoping for a sea change in public opinion, they were setting their sights too high.

“But the bad news for Trump is that they are not convincing anyone that he is innocent either,” he added.

Tobe Berkovitz, a Boston University professor who specializes in political communications, argued that the battle for public opinion will come down to an extremely narrow swath of voters.

“For the majority of voters, their decision about impeachment is already baked,” he said. “Most voters are highly partisan and that partisanship has created a perspective as they watch the impeachment proceedings.”

Barring some massive revelation, he added, “it is going to be exceedingly difficult” to move a large number of voters.

Trump himself is sure to continue to batter the inquiry and hope he can erode the public’s opinion of it.

“If the president fared this well through an accusation being made, and we already know the outcome to the [Senate] trial, than I think he can scream all over the place that this is a partisan witch hunt,” said Blakeman.

The Memo is a reported column by Niall Stanage, primarily focused on Donald Trump’s presidency.