Could how Democrat Tom Suozzi campaigned on immigration help his party win nationally?

After former Democratic Rep. Tom Suozzi won the special election in New York's 3rd Congressional District this week by campaigning on more border security, other Democrats are saying the takeaway message is that their party needs to go "on the offense" on immigration.

The issue was a flashpoint of the special election, especially as migrant encounters at the U.S.-Mexico border reached a record high of 302,000 in December and apprehensions hit a historic peak of 2.2 million in fiscal year 2022. Over 100,000 migrants have been transported to Democrat-led cities like Washington, Chicago, Los Angeles and New York.

Some point to other factors that helped Suozzi -- such as his name recognition in the district -- but say his win still might offer a playbook for the path forward for Democrats on an issue the party has struggled with.

Rep. Adriano Espaillat, D-N.Y., appearing on a press briefing Wednesday with Democratic strategists, called Suozzi's victory "a sign that the best defense is a strong offense … speaking right in front of it directly through the center and talking about not just border security, but opening up pathways to legal migration … is an argument that the American people will embrace," Espaillat said.

Facing attacks from his opponent Mazi Pilip over what she called Democrats' failed border policies, Suozzi stressed during his campaign that he supported both tightening immigration laws and finding a bipartisan compromise, including supporting a failed deal recently announced in the Senate.

"With immigration, with me, it's about pushing for a bipartisan compromise that'll will actually address the problem we face of closing the border, trying to stem the tide of what's happening, and [to] treat people like human beings," Suozzi said at a news conference two days before the election.

"Ducking the issue is a mistake. Suozzi hit it head on," said veteran New York Democratic strategist Hank Sheinkopf.

Mo Kantner, senior director of policy and research for nonprofit research and advocacy group American Immigration Council pointed to Suozzi's win as proof that "immigration doesn't have to be a wedge issue; one can stand for an orderly, efficient process at the border that is also fair and humane."

Kantner also added that the topic of immigration goes beyond just border issues, saying that "Every state in the country is impacted by immigration," she said.

And Democrats in Washington are taking a similar tone.

The Democratic National Committee, in a memo released after the election, pointed to the results as showing that Democrats "are winning on the issues that matter to voters," including the border, pointing to Donald Trump's criticism of the border deal that helped sink its support in Congress.

"From rooting for the economy to crash to tanking the border deal, Trump keeps showing the American people that his only real priority is helping himself -- and voters will hold him accountable come November, just like Trump himself admitted they should," DNC National Press Secretary Sarafina Chitika wrote in a statement to ABC News.

The House Majority PAC said in a memo released Wednesday about the special election results, was more explicit about how Democrats should campaign about immigration.

The group said that its internal research showed that Democrats did better "when they went on offense" to speak about the economy during the 2022 midterm elections. "Democrats must do the same on immigration," the group wrote, adding that Democrats should "hammer" Congressional Republicans over the failure of the border security bill.

The House Majority PAC spent around $7 million to support Suozzi's bid, according to an analysis of Federal Elections Commission records by OpenSecrets.

Sen. Chris Murphy D-Conn., in a memo to Democratic colleagues on Wednesday obtained by ABC News, said that Suozzi's win "can serve as a roadmap for Democrats. Suozzi messaged aggressively on the issue … and [he] turned what could have been a devastating political liability into an advantage."

"Quite simply, we risk losing the 2024 election if we do not seize this opportunity to go on offense on the issue of the border and turn the tables on Republicans on a key fall voting issue."

Suozzi's success may be tied in part to local factors that would not be the case nationally, both in terms of and separate from immigration issues.

"It's the political equivalent of what the weathermen call a wintry mix," Lawrence Levy, executive dean of Hofstra's National Center for Suburban Studies, told ABC News.

Suozzi may have succeeded thanks to many local factors, Levy said, including his longtime record of being a moderate on many issues, his name recognition – having served in the seat before and in local office – and that he managed to bring together a variety of different groups within the Democratic voting bloc to support him.

Sheinkopf, too, warns about the White House and its orbit mining too much meaning from Suozzi's win.

"Democrats shouldn't generalize from this outcome. Suozzi had 100 percent name recognition. He won handily. It was about him, not about issues. Advice to Democrats: every district race will be different. Trends matter less than candidates and their individual relationships with the communities they serve or hope to serve," said Sheinkopf.

That's a sentiment acknowledged by some Democrats as well, even when they discuss immigration's role in the race.

"Tom Suozzi worked on immigration issues with me when he was a county executive … he knows this issue and he knows his district better than anybody else. And so whatever political decisions he made, I'm sure took into consideration the realities of his district," Espaillat said on the press call.

Levy also highlighted that those realities in the district include how there is a "gap between perception and reality" regarding the reality of migrants in New York's 3rd Congressional district, which has not seen an influx of migrants – but people have seen news stories on New York City media market television or have seen migrants when they commute into the city.

"The Republicans had been pretty adept…at widening that gap between perception and reality, and exploiting it by tying immigration to an issue that had worked very well for them the last few election cycles, which is crime," Levy said, until Suozzi started "punching back."

But regardless of what's happening on the ground in the district, Levy said that in districts similar politically to the relatively suburban one that Suozzi won, being on the offensive as he was on border issues could "play well."

"But in addition to a message, you need a mouthpiece," Levy said. "Somebody who is able to sell it; who has the credibility with the voters, someone who they know. someone who they respect; even if they disagree."