LAS VEGAS — Pete Buttigieg is pitching himself as a rare Democrat who can win over GOP voters in a general election, a Midwesterner whose message of national unity and healing can convert President Donald Trump’s supporters into “future former Republicans.”

The phrase is a staple of Buttigieg’s stump speech, usually drawing cheers from his growing crowds. He bolsters it in a new TV ad in Nevada, telling voters his campaign sees “Democrats hungry to win, independent voters who had been turned off by our politics, Republicans tired of trying to look their kids in the eye and explain this presidency, all standing together.”

But national polls suggest Buttigieg doesn't have much appeal to Republicans in a one-on-one race against Trump, a data point that clashes with an important part of his courtship of Democratic primary voters. Trump retains overwhelming support among Republicans and is cruising to renomination.

Though Trump is toxic to Democrats and vulnerable among independents, his high party approval rating suggests GOP voters aren't shopping for alternatives inside or outside the tent, despite the wishes of many critics.

Buttigieg earned the support of just 5 percent of self-identified Republican voters in a potential matchup with Trump, who garnered 92 percent in a new NPR/PBS NewsHour/Marist survey taken after Buttigieg tied for first (with Bernie Sanders) in Iowa and finished second in New Hampshire.

His rivals didn't fare much better with Republicans — Mike Bloomberg had 8 percent, Joe Biden had 7 percent, and Sanders and Amy Klobuchar had 6 percent each. Overall, Biden performed best against Trump with 6-point lead; Buttigieg led Trump by 2 points, within the poll’s margin of error.

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A new NBC/Wall Street Journal poll out Tuesday found Buttigieg winning just 9 percent of Republicans in a one-on-one race with Trump. Sanders also had 9 percent, while Biden had 10 percent. Overall, Biden led Trump by 8 points, while Sanders and Buttigieg each led the president by 4 points.

In 2016, Hillary Clinton won 8 percent of Republican while Trump won 88 percent, according to exit polls.

In new swing-state polls testing how Democrats perform against Trump, released Thursday by Quinnipiac, Buttigieg carried 6 percent of Republicans in Michigan, 5 percent of Republicans in Pennsylvania and 4 percent of Republicans in Wisconsin. Overall, Buttigieg performed a bit worse than the strongest Democrats against Trump in the battleground states, leading by 1 point in Michigan and 4 points in Pennsylvania, while trailing by 8 points in Wisconsin.

Even though Buttigieg lacks GOP appeal in surveys, many Democrats believe he's electable, which helps him in the race for the nomination ahead of tougher contests in Nevada and South Carolina.

“He has integrity, he has good ideas, and moderate enough positions that I think he's electable,” said Nikki Levin of central Massachusetts, who plans to vote for Buttigieg in the state's March 3 primary. By contrast, she said she worries that Sanders and Elizabeth Warren are “too far left for the general electorate.”

In Iowa, where Buttigieg achieved a groundbreaking delegate victory, entrance polls found that nearly two-thirds of caucusgoers were more motivated to pick a candidate who can defeat Trump than one who’s closest to them on issues. Buttigieg finished a close second in New Hampshire, where exit polls found that he outpaced all rivals with voters focused on defeating Trump.

A Buttigieg campaign aide noted that he won 21 of the 31 Iowa counties that flipped from President Barack Obama to Trump in 2016, and pointed to a New York Times/Siena survey of Iowa heading into the caucuses that showed Buttigieg performing among the best in the Democratic field with Republicans against Trump. (The survey still found him losing the state to Trump by 1 point.)

"Pete won in places that voted for Donald Trump in 2016, showing that voters turned off by this president are looking for a new generation of leadership," Buttigieg spokesman Ben Halle told NBC News. "In New Hampshire, Pete did the best in areas that saw the highest increases in turnout between 2016 and 2020, proving that he can expand the Democratic electorate in November."

The findings point to a disconcerting reality for Trump’s critics, many of whom hope Republicans will break with Trump in the November election and deny him four more years. While many Trump allies are privately aghast at some of his actions and words — with others publicly conceding he’s a poor role model for young people — they are still willing to support him to keep Democrats from power.

The lack of interest among voters in crossing party lines this fall indicates that the 2020 election will turn on which side can mobilize its base and appeal to independents. Sanders has a different theory of electability — one that hinges less on converting Trump voters than on mobilizing Americans who are disenchanted with the system and want a president who'll disrupt it.

Caleb Green, 26, an attorney in Las Vegas who is deciding between Warren and Sanders, said he's skeptical of Buttigieg’s pitch to Republicans and centrists.

“For some people it’s effective, but not for me personally," Green said at a Buttigieg address to the Black Law Students Association forum at the University of Nevada, Las Vegas. "I don’t believe that argument. A lot of things had to happen in 2016 for Donald Trump to win. He won in Michigan and Pennsylvania by very small margins. ...

"We should just put the best candidate forward, the person who best represents the Democratic Party."