The Trump 2020 campaign noticed something interesting while crunching data from its February rally in El Paso: A significant percentage of the crowd crossed into Texas from Las Cruces, New Mexico, including plenty of women and Hispanics, who will be pivotal to the president’s reelection prospects.

“That piqued our interest in New Mexico,” said Tim Murtaugh, the Trump campaign’s director of communications.

Mr. Trump will rally with supporters outside Albuquerque, the state’s largest city, on Monday as part of a bid to expand his 2016 victory map and win states that have tilted blue in recent presidential cycles.

Besides New Mexico, the campaign is eyeing New Hampshire, Colorado, Nevada and even Oregon, which has a libertarian streak and, the Trump team theorizes, could be stocked with voters sick of hyper-PC antics in liberal Portland.

Mr. Trump’s critics say his campaign is looking for insurance against leaking support in the Upper Midwest and elsewhere, though the campaign insists that’s not the case. The campaign says its operations in big states such as Ohio and Michigan are well-funded, so they are going to reach for more.

“Why would you not? If you think you can be competitive and win in any given state, why would you not take a shot at it?” Mr. Murtaugh said.

The campaign says New Mexico is a ripe target because Mr. Trump has a “good story to tell” about job creation there, especially in the petroleum industry.

Michael Glassner, chief operating officer of the Trump campaign organization, cited an “economic boom” in New Mexico when he announced the rally last week. He said the state has added 34,000 jobs since Mr. Trump took office.

The Rio Rancho event will be Mr. Trump’s third rally in New Mexico, though his first since 2016.

Analysts said Mr. Trump faces an uphill battle in turning the state red.

He lost New Mexico to Democrat Hillary Clinton by 8 percentage points in the 2016 presidential election, and Barack Obama won it comfortably in each of his presidential elections.

“Back in 2000 and 2004, New Mexico was truly a battleground state in which George Bush had two very close elections, one of which he won and one of which he lost. However, since then, the Democratic presidential candidates have won in New Mexico by very comfortable margins,” said Brian Sanderoff, president of Research & Polling Inc. in Albuquerque.

He said Mr. Trump’s fortunes will hinge on Hispanics, who account for about a third of the New Mexico vote in presidential cycles. As it stands, about 7 in 10 typically vote for the Democratic candidate, Mr. Sanderoff said.

His final polling from the 2016 cycle suggested that Mr. Trump grabbed 27% of the Hispanic vote and former New Mexico Gov. Gary Johnson, the Libertarian Party candidate, got 14%.

Mr. Trump will have to reel in some of that Johnson share in 2020 and find a way to garner 40% of the Hispanic vote to have a shot at winning New Mexico, Mr. Sanderoff said.

“Many Hispanics are liberal on economic issues and more conservative on social issues such as abortion,” he said. “I think the Trump campaign will attempt to sway the Hispanics on social issues and border security.”

He is right about the strategy.

The Trump team says it is confident that the president’s pro-life record is a winner with Hispanics, and they insist Mr. Trump can sway members of the bloc by posing a simple question: If you or your family members immigrated to the U.S. legally, shouldn’t others?

“They say, ‘Damn right,’” said Mr. Murtaugh. “We think significant numbers support the president’s approach to immigration, contrary to what Democrats believe.”

The Trump campaign is hoping to make inroads during National Hispanic Heritage Month. It held a training session Thursday for volunteers in Houston ahead of the Democratic primary debate in the city, and it plans to follow up Mr. Trump’s rally with a “Vamos to Victory” event in Albuquerque on Tuesday.

Campaign manager Brad Parscale and other top campaign figures will appear at the session.

Rep. Ben Ray Lujan, a Hispanic Democrat running for an open Senate seat in New Mexico, responded to the announcement of the president’s rally in Rio Rancho by tweeting that “his values are not our values.”

The Democratic National Committee, meanwhile, said it has no intention of losing steam in New Mexico after a good showing in the midterm elections.

“Last cycle, Democrats crushed Republicans in New Mexico because voters are fed up with President Trump’s toxic health care agenda and broken promises,” said David Bergstein, the DNC’s spokesman on battleground states. “We take nothing for granted, but this GOP strategy looks like they’re concerned about a realistic pathway to 270 electoral votes.”

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