The Republican State Convention is giving party leaders a chance to test messages about crime, inflation and Democratic leadership.

By Katie Glueck and Nicholas Fandos

GARDEN CITY, N.Y. — Four months after Republicans scored upset victories around the country and in local races across New York, the state’s party leaders gathered at a plush hotel in a Long Island village this week, painting a bleak picture of life under Democratic rule.

Gas prices are spiking, and groceries are pricey. Concerns around crime are reordering politics in major cities at home, and Americans are shaken by images of war abroad. Debates around mask mandates and curriculum have turned school board meetings into political battlegrounds.

“People are very, very unhappy,” said Bruce Blakeman, the Nassau County executive and one of a number of Republican candidates who unexpectedly defeated Democrats in races across Long Island last fall. “That usually bodes very poorly for the party in power.”

Across the nation, Republicans are preparing to test how deep into liberal territory they can push in the midterm campaigns, at an exceptionally challenging moment for President Biden and his party.

If they can make real inroads in New York after years in the political wilderness, the thinking goes, that will offer a clear indication of a political wave underway.

One major measure will be the governor’s race. On Tuesday, Representative Lee Zeldin, a Long Island Republican, was named his party’s designee with 85.25 percent of the vote at its state convention.

If he wins the June 28 primary, his candidacy will offer a vivid test case of a major challenge for many Republican candidates in New York and other Democratic-leaning states: navigating the balance of first appealing to a primary electorate that embraces Mr. Trump, and then to a broader electorate that has firmly rejected him.

Mr. Zeldin has a legislative track record that includes voting to overturn the 2020 elections results and opposing the creation of an independent commission to probe the Jan. 6 attack on the U.S. Capitol, explosive liabilities in a general election in New York.

On Tuesday, he brushed off questions about those dynamics, suggesting voters are more focused on matters of the economy, education and public safety. He sought common cause with frustrated Democrats and touted a diverse slate of Republican candidates.

“We’re going to keep showing up to your communities to earn your votes,” pledged Mr. Zeldin. “We are all hitting our breaking points.”

He boldly predicted a coming “red tsunami,” one more example of the political wave imagery Republicans deployed throughout the convention, complete with a surfboard display outside the ballroom-turned-convention hall. Inside, party leaders endorsed candidates for major offices and road-tested messages about crime and bail, education and rampant inflation while offering broader indictments of Democratic leadership.

“You could have people getting buried that don’t think they have a race today,” Nicholas A. Langworthy, the chairman of the New York Republican State Committee, said in an interview. “This is a hurricane coming at our back. People are really pissed off.”

Just where the high-water mark for Republicans reaches remains to be seen. A Republican has not won a statewide race in New York since George E. Pataki secured a third term as governor in 2002, a now-distant era of consensus politics.

In the years since, Democrats have amassed a more than two-to-one advantage in party registration, making it difficult for Republicans to attract viable candidates in key races for Senate and attorney general.

And while there was an overwhelming demonstration of institutional support for Mr. Zeldin on Tuesday — attendees sported orange Zeldin shirts and he was drowned out at times by cheers — there were also signs of discontent.

The businessman Harry Wilson, who made a name turning around companies, entered the race last week and has said he will spend roughly $10 million of his own money in the campaign. And Rob Astorino, the former Westchester County executive, took oblique swipes at years-old remarks Mr. Zeldin made in praise of former Gov. Andrew M. Cuomo.

Both men received around 7 percent of the vote, and both pressed arguments around their abilities to win a general election. Only Mr. Zeldin met the delegate threshold for a spot on the ballot, so other contenders will have to petition their way onto the ballot.

“All the issues are with us,” Mr. Astorino, the 2014 nominee for governor, said in an interview. “We just have to make sure that the Republicans have the most qualified and electable candidate in November.”

New York Democrats quickly sought to brand Mr. Zeldin as “Big Lie Lee,” while national Democrats also made it plain that they will seek to tie Mr. Zeldin to Mr. Trump.

“Lee Zeldin has consistently shown his loyalties lie with Donald Trump, not New Yorkers,” Christina Amestoy of the Democratic Governors Association said in a statement.

But at the Republican State Convention and in interviews with party officials, candidates and strategists, Republicans signaled that they see opportunities not only to compete in the governor’s race but also to outperform expectations in congressional and state legislative districts from Long Island to Rochester that usually favor Democrats.

Their plan for races in Democratic-leaning areas goes like this: Keep the focus on matters of public safety, cost of living, education and in some cases coronavirus-related mandates. Make the midterms a referendum on Democratic leadership in Washington and Albany. Engage constituencies, including Asian American and Latino voters, that have been receptive to Republicans. And capitalize at every turn on a brutal political environment for the Democrats.

A recent Washington Post-ABC poll found that Mr. Biden’s national approval rating was at 37 percent. Even in New York, Mr. Biden’s favorability rating was the same as his negative rating — 48 percent — his lowest levels since taking office and a striking result in one of the most heavily Democratic states in the country, according to a recent Siena College poll of registered New York voters.

The Republican convention unfolded against the backdrop of devastating images from Russia’s invasion of Ukraine. Several speakers sought to paint national Democratic leadership as weak on the international stage, though Mr. Trump has put Republicans in a bind by lavishing praise on President Vladimir V. Putin of Russia.

“We need a change in Washington,” Mr. Pataki said on Monday, assailing the Biden administration’s stewardship of the crisis.

Some of Mr. Pataki’s allies had hoped he would consider another run for governor. Mr. Pataki, 76, did not firmly rule out such an idea, but he did tell reporters he expected one of four contenders to emerge as the nominee: Mr. Zeldin, Mr. Wilson, Mr. Astorino or Andrew Giuliani, the son of the former New York City mayor Rudolph W. Giuliani.

The race appears to be in flux, with the recent Siena poll showing Mr. Zeldin and Mr. Astorino as largely unknown quantities. Mr. Giuliani, perhaps because of his famous last name, was more polarizing, with a favorable rating of 47 percent among Republicans but a matching unfavorable rating among voters overall.

He significantly trails Mr. Zeldin and Mr. Astorino in fund-raising, according to the last campaign finance disclosure.

Mr. Giuliani said that his father, whose zealous efforts to overturn the 2020 election results have made him a pariah among many New Yorkers, would campaign for him in coming weeks, and he offered an apparent defense of his father’s actions onstage after the two made the rounds in the hotel lobby.

Mr. Giuliani — who branded Gov. Kathy Hochul “Crime Wave Kathy” — was warmly received, but he secured only .75 percent of the vote at the convention.

Whatever the primary result, Ms. Hochul, the likely Democratic nominee and a relative moderate, would be a formidable opponent.

“That’s going to be much tougher for Republicans, notwithstanding that the congressman, Lee Zeldin, is a very fine person,” said former Senator Alfonse M. D’Amato, a Republican. “The Trump business, though, is going to hurt him.”

Mr. Wilson is viewed privately by some Democrats as a stronger general election contender, but it has often been difficult for candidates who did not support Mr. Trump to survive Republican primaries. Mr. Wilson voted for him in 2016 but wrote in Nikki Haley, the former ambassador to the United Nations, in 2020, he said.

Mr. Wilson, the party’s 2010 nominee for comptroller, cast himself as a political outsider with a strong business record — “someone with a fresh perspective, someone who can channel our anger for change, not just yell the loudest,” he said.

Representative Tom Reed, a Republican in the state’s Southern Tier, said he was concerned that his party was headed for a messy primary that could undercut its chances in a race for governor that is already an “uphill battle.”

“My hope is that it’s not bloody,” said Mr. Reed, who was contemplating his own bid for governor before he was accused of inappropriately touching a lobbyist. “Because we all know winning the governor’s office in New York is a very, very difficult path to traverse for a Republican, even in a wave year.”