Miami Mayor-elect Eileen Higgins believes the key to her election victory Tuesday — the first for a Democrat in almost 30 years — was her outreach to people of all political persuasions.

In an interview on CBS News just after the election, CBS News chief Washington correspondent Major Garrett asked her about the "Trump effect;" President Trump had endorsed her Republican opponent, drawing attention to the race.

"I don't know," Higgins responded. "What I know is what I did. I worked. I knocked on doors and called Republicans, independents and Democrats all across the city of Miami — because you cannot become the mayor of this city if only Democrats vote for you. You can't become the mayor of this city if only Republicans vote for you. You've got to have all three."

Higgins, who is also the first woman elected to be Miami mayor, won 59% of the vote Tuesday. She also pointed out that she has served for eight years on the county commission in the city, where she represents a Republican-leaning district.

A former Miami-Dade County commissioner, Higgins defeated Republican candidate Emilio González, a former city manager who had been endorsed by both President Trump and Florida Gov. Ron DeSantis, in a runoff election. The mayoral race is officially nonpartisan, but it grew more politicized because of the Trump administration's immigration policies and Mr. Trump's endorsement of her opponent. 

She said that her political party won't matter as she takes on the responsibilities of the office.

"The folks of the city of Miami know that I am a loud, proud Democrat," she continued. "But when I get elected, the election's over, and the time of service begins, and you serve everybody. Never, ever ask their political affiliation. If their street is flooded, if they need an affordable unit to live in, you don't ask what party they're from. You say, 'Yep, we've got to figure out how to make that happen for you.'"

Though Democrats nationwide were encouraged by the outcome of the Miami race and the elections in November, Garrett asked Higgins whether there's a risk that national politicos were reading too much into the results. 

"I think it's always important to look at the place, right?" she said. "I think we saw that in the elections in November and then here, what the folks in New Jersey and Virginia and New York chose, they chose the person they thought would be right for them. And that's the same thing that happened here in Miami."

Higgins focused on critical local issues, including immigration, housing affordability, flooding and city growth. Miami is heavily Hispanic, and a majority of residents were born outside the U.S. She spoke of some of the Miami residents whose families have personal experience with the Trump administration's immigration crackdown. 

"Folks will whisper in my ear — it's always a whisper, they're afraid," she said. "'They took my brother. I don't know what happened to my uncle.' Sometimes it's Alligator Alcatraz. Sometimes they have no idea where their relatives are. That's not the way it's supposed to be in America."

Higgins advocates strong border security and told Garrett, "We want to know who's coming and who's going, so no criminals are getting into our country."

"That isn't what they're doing. They said they were going to go after criminals and now they're going after those relatives and neighbors, and doing it in such a way that in my opinion is obviously inhumane, but also a real, real threat to the economic vitality of southern Florida," Higgins said. 

During her campaign, Higgins also touted the work she's already done on housing affordability. She told Garrett that during her tenure on the county commission, she examined county-owned property to determine whether it could be used for housing. 

"I said, 'What's on that property? What can be on that property? Let's build housing when it's appropriate.' And I have already opened thousands of units of affordable housing, sometimes low income seniors, sometimes working families." She said thinks that experience is "a big reason" that people voted for her. 

"We started with 13 candidates in the race," Higgins said. "I was the only candidate with a history and a track record of building thousands of units ... I know how to make sure we can accelerate the construction housing that people can afford."

Watch the full interview on "The Takeout," on CBS News 24/7. Download the free CBS News app.