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It is one poll in one state and therefore not a definitive reading of public opinion. But the latest survey from Marquette University’s law school of attitudes in Wisconsin highlights one of the challenges Democrats face as they move steadily toward impeaching President Trump.

The survey was released as the House Intelligence Committee was taking public testimony from current and former administration officials. The testimony offered a consistent conclusion — that the president was seeking help from the government of Ukraine to harm a potential political rival (former vice president Joe Biden) while $400 million in military aid and a White House meeting for Ukraine’s new president were being held up.

The testimony was damaging to the president. But the Wisconsin survey showed modest but nonetheless perceptible shifts in the direction favoring Trump, on the question of whether he should be impeached and also in head-to-head matchups against leading Democratic presidential candidates. What makes the Wisconsin poll important is that it is a snapshot of a state that, more than any other in the country, could decide the 2020 election.

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The Marquette poll found 40 percent of registered voters favoring impeachment of Trump and his removal from office, compared with 44 percent in October. At the same time, 53 percent oppose impeachment and removal, compared with 51 percent the previous month.

Statistically these are tiny-to-insignificant shifts, but the direction of the changes on this and other questions are consistent. From one month to the next, Republican attitudes hardened ever so slightly in favor of the president. As Charles Franklin, who directs the poll, put it, “A Republican rally around Trump is very strongly demonstrated in the poll.”

Meanwhile, Democratic attitudes, while still overwhelmingly in favor of impeachment and removal, softened slightly. Support for impeachment among independents went from a margin of 22 points to a margin of 11 points.

Franklin pointed to another set of findings showing that 42 percent of registered voters saying Trump did something “seriously wrong,” 9 percent saying he did something “wrong” and 38 percent saying he did “nothing wrong.” He called that “the even split we see in Wisconsin politics.”

© Saul Loeb/AFP/Getty Images Trump supporters listen to the president at the Green Bay rally. The survey was conducted Nov. 13-17, which means it began the day of the testimony by William B. Taylor Jr., the senior diplomat in Ukraine, and concluded after testimony from Marie Yovanovitch, the former ambassador to Ukraine who was removed from her post last spring on orders from the president. The survey, with a margin of error was plus-or-minus 4.1 percentage points, was completed before this past week’s testimony, including that of Gordon Sondland, the U.S. ambassador to the European Union.

The results from Wisconsin also showed that, since the summer, the Democratic candidates have seen clear slippage in their support in hypothetical matchups with the president. Former vice president Joe Biden led the president by 51 percent to 42 percent in August. By October the margin was 50 percent to 44 percent. The latest poll flips the script. Trump now is ahead of Biden by 47 percent to 44 percent. The shift came primarily from movement among independents, either away from the former vice president to Trump or to a posture of saying they liked neither candidate.

Similar shifts have taken place in matchups between Trump and other potential Democratic challengers. Trump leads Sen. Bernie Sanders (I-Vt.) by 48 percent to 45 percent. He is ahead of Sen. Elizabeth Warren (D-Mass.) by 48 percent to 43 percent after being in a dead heat with her previously. South Bend, Ind., Mayor Pete Buttigieg, who has risen among Democrats in Iowa and New Hampshire surveys, is trailing the president by 47 percent to 39 percent.

Franklin described the findings on Biden, Sanders and Warren (Buttigieg was not included in the previous poll) as a shift from what was “a modest, mostly inside the margin of error” advantage for the Democrats to “a modest, mostly inside the margin of error” advantage for the president. He added, “That’s what you would expect in a battleground state.”

On the electoral college map, Wisconsin might be considered the quintessential battleground state heading into 2020. Its current political culture and partisan divisions are a microcosm of the nation. The divisions long predated Trump’s presidency but began to intensify during former Republican governor Scott Walker’s two terms in office and more so the past three years.

The 2000 presidential election saw the state go Democratic by two-tenths of a percentage point. The 2004 presidential elections tipped to the Democrats by four-tenths of a point. Barack Obama proved to be an anomaly, winning the state in 2008 by double-digits and in 2012 by about seven points. After Obama, Wisconsin reverted to its earlier status as a true battleground. Trump carried it by eight-tenths of a point, about 23,000 votes.

Trump’s current approval rating in the state, according to the Marquette poll, is 47 percent — higher than his national number and about the same as it was in the poll in October. Republicans are more unified behind him today than they were when he first ran for president.

Wisconsin has settled into a rough parity in partisan identification. Where once there was a modest Democratic advantage in party identification among voters, today it is basically even. It is also a state in flux politically, reshaped by the same forces and changing voter coalitions that are changing politics in other states.

The urban-rural divide has widened in recent years. Rural areas in Wisconsin, as in many other states, have become more Republican, especially during Trump’s presidency. Meanwhile, Democrats have made gains in suburban counties in Wisconsin that once voted strongly Republican.

© Saul Loeb/AFP/Getty Images President Trump claps during a campaign rally on April 27 in Green Bay, Wis. Counties around Milwaukee still favor Republicans but not by the margins of the past, as evidenced by the midterm election returns in 2018. Walker did worse in his home areas in southeast Wisconsin in 2018 than in his previous campaigns but better in rural areas in the northwest. The slippage in suburban areas has become a cause for concern among some Republican strategists who work the state regularly.

Wisconsin is one of three states of critical importance in 2020, the others being Michigan and Pennsylvania. All three went for Trump after consistently supporting Democratic nominees in a string of elections. If nothing else changes on the electoral map, which is to say if Trump again wins Florida, Ohio, North Carolina and Iowa, Democrats need the three northern states to capture the presidency or find substitutes elsewhere.

Of those three, Wisconsin could be the most difficult to covert. All three states now have Democratic governors, but Wisconsin’s Tony Evers won in 2018 by a percentage point over Walker; Michigan’s Gretchen Whitmer and Pennsylvania’s Tom Wolf both won by double digits. Wisconsin’s population is whiter than the other two. Wisconsin’s union infrastructure, a valuable source of voter mobilization help, has deteriorated, thanks to Walker’s assault on public employee unions.

Democrats in Congress are moving forward to impeach the president and leaders have said that constitutional prerogatives, not political considerations, should shape the proceedings. But there will be political fallout, which is why attitudes from Wisconsin bear watching. Much can change in the weeks and months ahead, but the modest shifts in the past month are a reminder to Democrats that public opinion is not currently moving in their direction.