President Trump won more than a third of Hispanic voters in Texas in 2016, but only a little more than one-fifth say they would vote for him in 2020, according to a new massive poll of battleground states.

Mr. Trump’s hurdle is even higher in North Carolina, where his 40% of the Hispanic vote in 2016, according to exit polls, has fallen to 18% support for reelection in 2020, according to Equis Research, which is conducting an ongoing study of Hispanic voters.

The chief takeaway so far is that Mr. Trump faces major headwinds.

The 2020 election “will be a game of margins, just as 2016 was, and the share of Latinx voters is growing in battlegrounds,” said Stephanie Valencia, co-founder of Equis Labs. Latinx is a gender-neutral term some use in place of Latino and Latina.

Equis sponsored polling in 10 states and found that in each of them, Mr. Trump’s support has slid since 2016.

In some states, it was only a small drop.

In Florida, his 35% share of Hispanic votes in 2016, according to exit polls, has slipped to 34% support in the new survey matching Mr. Trump to a generic Democratic candidate. Another 14% said they were undecided or picked another candidate, suggesting some room for the president to grow and perhaps top his 2016 performance.

Yet other states look grim.

Hispanics make up a small portion of voting in Wisconsin, one of the key Rust Belt states that provided Mr. Trump with his margin of victory in the Electoral College. But those voters are still souring, with Mr. Trump’s support falling from 34% in the last election to 13% in the poll.

In Michigan, where Hispanics are 4% of the population, he’s lost more than half his support, falling from 38% of the vote in 2016 to 17% in the poll.

The Trump campaign brushed off the numbers.

“What a surprise, a new liberal group finds exactly the results they went looking for,” said Tim Murtaugh, the communications director for the president’s reelection bid. “The president is doing well with Latino voters and will be reelected.”

Mr. Trump, on the campaign trail, says Hispanic voters should be thrilled with him because of the rising economy.

The Equis polling does show some good news for him on that front, with voters giving him decent marks for his handling of the economy.

They’re less excited about his immigration policy and his approach to health care, where Hispanic voters are pro-Obamacare, and even ready to embrace a “Medicare for All” government-run system, the polling found.

Equis said 32 million Hispanics will be eligible to vote next year, making them the largest racial or ethnic voting bloc.

Equis said if Mr. Trump can limit his losses among Hispanics, he could win reelection.

Ms. Valencia said one worrisome sign for Democrats was the gap between motivation and excitement in voting next year. In Colorado, for example, 78% of Hispanics told the pollsters they’re “very motivated,” but just 48% said they’re “very excited.”

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