The nation’s large and diverse group of Hispanic voters is showing signs of dividing its support between Democrats and Republicans more evenly than in recent elections, a new Wall Street Journal poll finds, a troubling development for the Democratic Party, which has long counted on outsize Hispanic support.

One year after giving Democratic House candidates more than 60% of their vote, according to polls at the time, the Journal survey found that Hispanic voters are evenly split in their choice for Congress. Asked which party they would back if the election were today, 37% of Hispanic voters said they would support the Republican congressional candidate and 37% said they would favor the Democrat, with 22% undecided.

Hispanic voters were also evenly divided when asked about a hypothetical rematch in 2024 of the last presidential contenders, with 44% saying they would back President Biden and 43% supporting former President Donald Trump. In 2020, Mr. Biden won 63% support among Hispanic voters, nearly 30 points more than Mr. Trump, according to AP VoteCast, a large survey of the presidential electorate. Hispanic voters account for about 1 in 8 eligible voters and are one of the fastest-growing groups in the electorate, factors that compound Democratic fears about any deterioration in support. “Latinos are more and more becoming swing voters.…They’re a swing vote that we’re going to have to fight for,’’ said Democratic pollster John Anzalone, whose company conducted The Wall Street Journal Poll along with the firm of Republican pollster Tony Fabrizio. Messrs. Anzalone and Fabrizio said the poll showed that economic issues were the main concern among Hispanic voters, drawing Hispanic men, in particular, toward the GOP.

Hispanic voters in the survey ranked economic issues as the priority for Mr. Biden and Congress to address. Hispanic men said Republicans had the better economic policy, by a margin of 17 points. Hispanic women, by contrast, said Democrats had better economic plans, by a 10-point margin. A majority of Hispanic men said they would like to return to the policies that Mr. Trump pursued as president, while a majority of Hispanic women said they would rather stick with Mr. Biden’s policies.

Strategists in both parties have been working since the 2020 election to calculate the size of the shift among Hispanic voters to the GOP and to understand its causes. One in-depth study, by Catalist, which compiles and analyzes voter data for Democratic candidates and progressive causes, found that Hispanic voters swung toward Mr. Trump by 8 points compared with 2016 in the two-party vote. Shifts in some parts of the country were larger. In its analysis of the 2020 electorate, Equis Labs, which studies the Latino electorate, found swings toward the GOP of 20 points in parts of Florida’s Miami-Dade County; of 12 points in the Rio Grande Valley of Texas; and double-digit swings in parts of the Northeast. In South Florida, the shift was big enough to flip two congressional seats to the GOP, the firm concluded. Analyses by various groups have cited a range of causes for the shift, including higher turnout among the most conservative Hispanic voters, GOP success in persuading voters who turn out infrequently and frustration over job losses due to pandemic-related business shutdowns. In last month’s election for governor in Virginia, AP VoteCast found that Republican Glenn Youngkin, who won the race, outpolled his Democratic opponent among Hispanic voters. In the Journal survey, Hispanic voters had a negative outlook on the economy, with 25% saying it was headed in the right direction and 63% saying it was headed in the wrong direction. That 38-point gap compared with a 31-point gap among all voters.

Hispanic voters saw Republicans in Congress as better able than Democrats to handle some economic issues, such as reining in inflation and cutting the federal deficit. They also saw Republicans as best able to secure the border. The Hispanic voters saw Democrats in Congress as better able to control the Covid-19 pandemic, rebuild infrastructure and make healthcare more affordable. The results showed Hispanic voters differing little from the overall electorate in their political preferences. Hispanic voters mirrored the overall voter pool, for example, when asked how Mr. Biden was handling his job. Some 42% approved of the president’s job performance and 54% disapproved—in line with the 41% approval and 57% disapproval among the broader voting public.