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 clearly 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.

Republicans overtly and implicitly embraced that imagery at their state convention that began on Monday — a surfboard was even displayed outside the convention hall. Inside, party leaders endorsed candidates for major offices and road-tested messages about crime 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, fueled in part by antipathy toward former President Donald J. Trump, and have locked-in congressional and legislative districts that could fortify them this fall.

Republicans have struggled to attract viable candidates in key races for Senate and attorney general. And many of their contenders face the difficult balancing act of first appealing to a primary electorate that embraces Mr. Trump, and then to a broader electorate that has firmly rejected the former president.

“Republicans are spending time creating false narratives to blame Democrats for these problems, but I think people are going to vote for the party that is working to find and enact solutions,” said Jay S. Jacobs, the chairman of the New York State Democratic Committee. “It’s March. We’ve got till November. And today’s reality is not going to be tomorrow's.”

But at the Republican State Convention and in interviews with party officials, candidates and strategists, Republicans made it plain 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 voters in New York.

The Republican convention unfolded against the backdrop of devastating images from Russia’s invasion of Ukraine. In a preview of how they may move to nationalize down-ballot races this year, several speakers made the war in Europe a central piece of their messaging and sought to paint national Democratic leadership as weak and feckless, 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, ripping into the Biden administration’s stewardship of the crisis in Ukraine. “We need a Republican Congress to hold this president accountable, we need a Republican Senate to hold this leader accountable, and to get the United States headed in the right direction.”

Some of Mr. Pataki’s allies had hoped he would head back toward Albany with another run for governor. Mr. Pataki, 76, did not firmly rule out such an idea on Monday, but he did tell reporters he expected one of four contenders to emerge as the nominee: Representative Lee Zeldin of Long Island; Harry Wilson, a businessman; Rob Astorino, the former Westchester County executive; 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, who has been named the presumptive nominee by party leaders, 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, but he cited his favorability ratings among Republicans as evidence of his ability to connect with voters.

Mr. Giuliani said in an interview 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.

Mr. Zeldin is favored to receive his party’s endorsement on Tuesday. But Mr. Wilson’s late entry into the race last week and the effort to draft Mr. Pataki to attempt a comeback point to some discontent around Mr. Zeldin, who has a long legislative track record in Albany and Washington that includes voting to overturn the 2020 elections results.

That could be a major liability in a general election against Gov. Kathy Hochul, the likely Democratic nominee and a relative moderate who some Republicans believe will be harder to beat than her predecessor, Andrew M. Cuomo, who resigned in disgrace, would have been.

Ms. Hochul is “a refreshing change from all of the nonsense that people were subjected to,” said former Senator Alfonse M. D’Amato, a Republican who said he has not yet decided how he will vote. “That’s going to be much tougher for Republicans, notwithstanding that the congressman, Lee Zeldin, is a very fine person, he’s done a good job. I think the Trump business, though, is going to hurt him.”

Asked about those dynamics, Mr. Zeldin argued that voters are animated by other issues and said he was focused on “reversing the attacks on wallets, safety, freedom and our kids’ education.”

But there is no question that Mr. Trump will be a factor both in the coming months of the primary and in the general election.

Mr. Wilson, who has pledged to spend roughly $10 million of his own money in the race, 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 make it through 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, is casting himself as an outsider with a record of turning around companies and a focus on matters of public safety, the economy and quality of life. He and Mr. Zeldin have both started spending on airtime.

“We desperately need capable, rational leadership in Albany,” he said.

Representative Tom Reed, a Republican in the state’s Southern Tier who is set to retire this year, 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, that it’s not negative and we get through it as quickly as possible and unite,” 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.”