Struggling to win over the Hispanics who helped power Republicans to victory four years ago, New Jersey gubernatorial nominee Kim Guadagno went the opposite direction Monday, embracing a Trump-like call to crack down on sanctuary cities in the state.

Several cities and counties, including Newark, were deemed sanctuaries this year by U.S. Immigration and Customs Enforcement, and Mrs. Guadagno, the lieutenant governor in Gov. Chris Christie’s administration, said she is determined to bring them to heel.

“If elected governor, I will pass a law to ban sanctuary cities so politicians can’t prevent law enforcement from turning violent and dangerous criminals over to federal immigration officials for deportation,” said Mrs. Guadagno, hoping to make up ground against Democratic nominee Phil Murphy.

It’s the same tactic that Ed Gillespie, the Republican candidate in Virginia, is using to try to close the gap against Democrat Ralph Northam. Virginia and New Jersey are the only two states with governor’s elections this year.

Polls show Mrs. Guadagno and Mr. Murphy running neck and neck among white voters, but Mrs. Guadagno trails by a massive margin among minority voters, which is likely to cost her the election barring a dramatic shift.

It’s a major drop-off from 2013, when Mr. Christie devoted plenty of attention to minorities and ended up winning about half the Hispanic vote en route to a resounding re-election.

Patrick Murray, director of the Monmouth University Polling Institute, said the 2013 race was an anomaly.

“A specific goal of the Christie campaign was to win the Latino vote in the exit poll in order to boost his ‘big tent’ selling point for 2016. Remember those days when the GOP was a sure loser if they couldn’t attract Latinos?” Mr. Murray said.

Republicans nationally came to that conclusion after the 2012 election, with the national party releasing an election autopsy report that called for embracing a softer line on immigration.

Mr. Christie appeared to heed the advice, vowing to back in-state tuition for illegal immigrant students. After his election, he made good on that promise, signing such a bill into law.

The moves helped him carry 51 percent of the Hispanic vote and 21 percent of the black vote, according to exit polls in 2013 — up from 32 percent of Hispanics and 9 percent of black voters in 2009.

The latest Monmouth University poll, however, finds Mr. Murphy leading Mrs. Gaudagno 71 percent to 16 percent among Hispanics and nonwhite voters.

Although Mr. Christie won women by 57 percent to 42 percent over state Sen. Barbara Buono in 2013, Mrs. Guadagno trailed by 25 percentage points in the Monmouth poll.

Among all voters, Mr. Murphy holds a 14-point lead.

Analilia Mejia, executive director of Working Families New Jersey, said she hates to give Mr. Christie credit for anything, but she said he earned it when it came to minority voters.

“He was intentional about trying to get the Latino vote and was campaigning in, wasn’t staying away from, communities of color,” Ms. Mejia said.

“But I think with Kim Guadagno, it is a much different time. She is running in a post-Donald Trump world,” she said. “The GOP is much different, and she is taking a page from the Trump playbook [by] targeting entire communities and painting them with broad, hateful brushworks, and she is trying to salvage a campaign that is in trouble.”

Mrs. Guadagno, a former prosecutor and county sheriff, said state and local law enforcement should be required to help federal immigration agents run checks to spot illegal immigrants booked into jails and prisons. She also said the governor should be allowed to withhold money from jurisdictions that refuse to cooperate.

Such a plan would be a tough sell in New Jersey, where Democrats control the legislature and have been more inclined to provide protections rather than sanctions against sanctuaries.

Mrs. Guadagno started zeroing in on the immigration issue last week, releasing a television ad accusing Mr. Murphy of having a soft spot for illegal immigrants and, by extension, the “backs of deranged murderers” — thereby jeopardizing public safety.

Mr. Christie this year said he supported federal efforts to strip sanctuary cities of grant money.

Mr. Murphy has pursued the “rainbow coalition” campaign strategy that worked for Barack Obama in 2008 and 2012, appealing to a broad range of demographic special interests.

He has appealed to women with his pro-choice stance, won the backing of gay rights groups and wooed black voters with promises to fight “voter suppression.”

Mr. Murphy has also said he would generally back illegal immigrants if they are in danger of entanglement with federal deportation officers.

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