People take selfies with Republican presidential candidate, Ohio Gov. John Kasich following lunch at Mike's Deli during a campaign stop April 7, 2016 in New York. (Bryan R. Smith/AP)

After Ohio Gov. John Kasich left and the mozzarella and cold cuts were cleared away, the registered Republicans in Mike’s Deli could be counted on one finger. Dave Greco, the manager, had packed the place, and photos of the governor carbo-loading had gone viral. Just as important, Greco had promised Kasich a true Bronx rarity — a Republican vote.

“A lot of people think I’m for Trump, because I’m opinionated, but Kasich is the right man for the job,” said Greco. “The first question I asked him was: ‘Are you gonna give your delegates to Cruz?’ And he said, ‘Absolutely not, absolutely not!’ That was what I wanted to hear.”

Kasich’s deli visit landed him in New York’s 15th Congressional District, which ranks as the most Democratic district in the country. Republicans are outnumbered 13 to 1 in this portion of the Bronx. But it still has three delegates to offer, like every other district in New York, which is why both Kasich and rival Ted Cruz campaigned here in recent days in their efforts to stay in the delegate hunt with front-runner Donald Trump.

The day before, Cruz, the firebrand senator from Texas, met with ministers and (unsuccessfully) dodged hecklers at a Chinese-Dominican restaurant.

New York’s GOP follows a modified winner-take-all formula.If any candidate wins more than 50 percent statewide, he takes all available delegates. If he falls below 50 percent, the second-place finisher is entitled to at least one delegate. The same is true in each congressional district — each of which gets three delegates, regardless of how many Republicans live there.

Republican presidential candidate Ted Cruz speaks to the media at the restaurant Sabrosura 2 on April 6, 2016 in the Bronx. (Bryan Thomas/Getty Images)

That has multiplied the power of Republicans in the 15th District, which packs more people than live in North Dakota into a few square miles between the Harlem River and Westchester Creek. As of 2013, there were just 41,760 registered Republicans in the Bronx, and only 13,468 in the 15th.

On election days, it gets worse. In 2012, Mitt Romney won just 3 percent of the 15th District’s vote.Even that was better than the party’s quixotic candidate for Congress, a piano tuner named Frank Della Valle, who won just 4,427 votes, or 2.5 percent of the total.

And that was a general election. In the 2012 presidential primary, conducted after Romney had basically wrapped up the nomination, just 1,682 Republican votes were cast in the entire Bronx. Kasich and Cruz, who acknowledge that Trump is ahead statewide, have complemented their Bronx visits with quiet outreach. Only voters who had registered with the party by October 2015 could vote, and it was a matter of working down a short list to find them.

“We’re getting massively positive earned media,” said Kasich strategist John Weaver. “We’re actively working that market for a variety of reasons; one of them’s the number of districts where we think we can get delegates. There are not a lot of Republicans voting there, but the ones who are we have a good shot at keeping or converting.”

But in conversations, Bronx Republicans said that Cruz’s campaign had done the most to reach them. “Cruz’s campaign was the only one that reached out to me,” Humberto Negron, 38, said after working a shift representing Republicans at the board of elections. “They wanted to sort of emphasize their values and their point of views, and that it’s reflective of the Bronx.”

Next up on the 2016 primary schedule: New York. So we asked, what if the candidates were New York City boroughs? (Peter Stevenson/The Washington Post)

From the outside, though, Cruz’s Bronx visit was a debacle. A stop at a charter school was scrapped after students announced a walk-out. Twelve hours before the candidate landed, his campaign called state Sen. Ruben Diaz Sr., a conservative Democrat whom Cruz had met at a banquet years earlier. Diaz assembled ministers to meet Cruz but couldn’t say how many of them were eligible to vote for him.

“I didn’t ask if you are a Republican or a Democrat or a Conservative,” said Diaz. The Conservatives are a party in New York that draws some of the most right-leaning voters. “Just the fact that Mr. Cruz gave respect will have a huge influence.”

In some cases, Cruz backers have hit a wall of Trump support. Party chairmen in 33 of New York’s 62 counties, including the Bronx’s John Greaney, have endorsed the mogul.

The party’s Bronx office had been set up next to a comic book store to reelect Mayor Michael Bloomberg in 2009. Since then, it has become monument to lost elections next to a comic book store. Maps of solidly blue districts share wall space with a sign for Joseph J. Savino, a former Bronx GOP chairman whose career peaked with a 22-point defeat in a state Senate race and bottomed out with a bribery conviction.

Bronx GOP Vice Chairman Mike Rendino, like Greaney, sustained lung damage on 9/11. He’d been a firefighter. Rendino ended that career early — he is 41 now — and took up managing a bar near Yankee Stadium. Cruz had reached out to him, too, but it struck him as pablum from “the biggest phony in politics.”

“Their pitch is more negative about Donald Trump than positive about themselves,” Rendino said. “Look, me and John both need treatment for what happened on 9/11. Cruz voted against the Zadroga [9/11 Health and Compensation Reauthorization] bill. He voted against Sandy relief. He said, back when he was talking about immigration, that ‘Manhattan is very concerned with its security with the Bronx.’ You don’t think that hurts us here?”

Rendino supports Trump — with the caveat that “half the crap he says” was hurting his campaign.

Rendino was joined in the Bronx office by two activists who have toiled in the area for years trying to expand the party, often in vain. Fred Brown, 80, ran the National Black Republican Council from a part of Manhattan that used to be in the 15th, and was trying to swing the organization behind Trump.

“We want Trump to come to the Bronx,” Brown said. “He has a lot to say about what he’s built here.”

“The Democrats haven’t done anything for us,” said Jose Acolon, 82. “They want us to think Donald Trump is anti-immigrant. Well, we know what’s going on. We just want to rebuild the Bronx.”

It was unclear whether Trump would visit the Bronx before the vote.

Meanwhile, the Cruz and Kasich campaigns were still looking for the handfuls of outnumbered Republicans who could get them delegates.

Joanna Bimonte, 49, was a Cruz supporter who’d “always been turned off by Trump,” and was angered anew when his campaign manager roughly grabbed a female reporter’s arm and denied doing so.

She was exactly what the Cruz campaign needed in the Bronx — an activist ready to go, ready to use her downtime between college classes to help.

“I have to figure out how to do that computer program thing that lets you make calls,” she said. “I’ll do that first. Then I’ll drive people to the polls. That can’t take too long. I mean, how many Republicans can there be here?”