Frank Curnow, a retired Navy veteran, had a question for the Republican Party volunteers at an early voting site in Daytona Beach, Fla., on Thursday.
Why, he asked, were some polls suggesting a tight race for the open seat in his reliably conservative congressional district, Florida’s Sixth?
“That’s not good,” said Mr. Curnow, 77, a registered Republican who voted for the party’s candidate, State Senator Randy Fine, because “he carries the Trump banner.” The race, he added, “is critical.”
Voters in the district, which includes the stretch of coast between St. Augustine and Daytona Beach, overwhelmingly voted for President Trump. But on Tuesday, they will cast ballots in what seems to be an unusually competitive contest to replace former Representative Michael Waltz, who stepped down to become Mr. Trump’s national security adviser.
[We’re tracking each party’s turnout ahead of Tuesday’s special House elections.]
Mr. Fine, who is facing Josh Weil, a Democrat and public school employee, is still widely favored to win. But with Republicans clinging to their House majority by just a few seats, it was clear this week that voters in the district are thinking about what the outcome of the race — and of another race for former Representative Matt Gaetz’s seat in the Florida Panhandle — could mean for Mr. Trump’s agenda.
“It’s important that we keep the seats,” said Doreen Colby, 74, a registered Republican who lives in Daytona Beach. “We want to make sure Trump can keep doing what he’s doing.”
After tapping Mr. Waltz and Mr. Gaetz for his cabinet, Mr. Trump quickly endorsed candidates to replace them. (Mr. Gaetz later withdrew from consideration as attorney general, but had already resigned from Congress.)
But while Jimmy Patronis, Florida’s chief financial officer, is expected to coast to victory in Mr. Gaetz’s former district, which is extremely conservative, some Republicans have expressed concern about the Sixth District race.
There are nearly twice as many registered Republicans as Democrats in the district, which Mr. Trump won in November by a two-to-one margin.
“We have a candidate that I don’t think is winning,” Stephen K. Bannon, Mr. Trump’s former chief strategist, said of Mr. Fine last week on his “War Room” podcast.
On Thursday, Mr. Trump held a telephone town hall for Mr. Fine, stressing his loyalty to the administration’s agenda.
“It’s not overstating things to say that your agenda is at stake in this election, and this district can’t let you down,” Mr. Fine told the president during the event.
Only one Democrat — former Senator Bill Nelson — has won the district in a federal race since 1989. Both Gov. Ron DeSantis, who held the seat from 2013 to 2018, and Mr. Waltz, who succeeded him, won it by double-digit margins.
In interviews this week, loyal Republicans in the district were largely complimentary of Mr. Trump’s first few months in office. They praised him for his aggressive immigration enforcement and applauded the deep cuts to the federal work force.
Their vote for Mr. Fine, they said, would send a message that Mr. Trump’s actions so far are what they wanted. Leaders in both parties “all talk about making cuts but none of them do it, and Trump is the first one to actually do it,” said Greg Bohr, 74, a Palm Coast retiree. “My theory is, give the guy a chance.”
For Democrats, despairing over how little legislative opposition Mr. Trump has faced, the special election is a chance to voice their displeasure.
“I’ve got to do something,” said Marcia Hopkins, 63. Before driving to cast her vote for Mr. Weil, she said she asked the construction crew working on her condominium if they had voted and offered them rides to a polling place. (No one took her up on it.)
Pointing to Mr. Fine’s high praise for Mr. Trump, Paul Hunt, 61, who works in real estate in DeLand, said of the candidate: “I don’t care if he was saving Bambi — based upon his affiliation, that tells me everything I need to know.”
Of Mr. Weil, whose campaign workers directly reached out to him, Mr. Hunt said, “He’s running at the right time.”
By Friday, Mr. Weil received an endorsement from Senator Bernie Sanders, the Vermont independent.
Mr. Weil, a public school teacher for a decade, has said if elected, he would prioritize expanding access to health care and education.
Mr. Weil has also emphasized his objections to cutting the federal work force and government assistance programs; nearly a third of the district’s population qualifies for Social Security. He has also worked to convince conservative voters that he would be a voice for them, too.
“People want a representative who will actually serve and represent them,” Mr. Weil said in an interview at Stetson University in DeLand. “They don’t need 200 carbon copies of a Republican Party clone all moving in lock step.”
By mid-March, Mr. Weil had brought in nearly $10 million, while Mr. Fine had raised less than $1 million. In the final week of the campaign, outside Republican groups have poured more than $1 million into television advertising for Mr. Fine; Elon Musk and his allies have pitched in money, too.
Despite the national investment and high-profile visits, officials in both parties are cautioning against parsing the race’s outcome for hints of how the electorate is feeling about Mr. Trump.
Should Mr. Fine not do as well as other Republicans have in the district, Mr. DeSantis told reporters on Tuesday, “That is not a reflection of President Trump — it’s a reflection of the specific candidate running in that race.” (Mr. Fine endorsed Mr. Trump over Mr. DeSantis in the Republican presidential primary last year.)
The race drew more attention last week after the editor of The Atlantic revealed that Mr. Waltz had accidentally included him in a group chat on the encrypted messaging app Signal, in which plans for attacks against Houthi rebels in Yemen were shared and discussed. Mr. Waltz has faced calls for his resignation, given the sensitivity of the military plans.
There is little indication, however, that the issue would register in the special election.
Some voters who supported Mr. Waltz in past elections downplayed what they perceived as an honest, if not slightly embarrassing, mistake. Others expressed confusion about what exactly had transpired.
“I have no idea what Signal is,” said Michelle Moyer, 49, who helps run her family’s wholesale sleigh bell business in South Daytona and voted for Mr. Waltz in November. What was more important, she said, was “filling Waltz’s seat with someone who is like-minded.”
“I appreciate that the country is going in the right direction,” she said, and Mr. Fine “agrees with the policies Trump is putting in place.”
On Thursday, Republican volunteers at the Daytona Beach polling place where Mr. Curnow voted kept a watchful eye on the early voting numbers. A man driving by rolled down his window to tell them that Representative Elise Stefanik of New York would stay in her seat, at Mr. Trump’s request, instead of becoming his ambassador to the United Nations.
“Yay,” Gisela Klobucar, one of the lead volunteers, said, clapping in reaction to the news.
She added, “We have one more person on our side.”
Eric Adelson contributed reporting from DeLand, Fla., and Abigail Geiger from Palm Coast, Fla. Theodore Schleifer and Ruth Igielnik contributed reporting from Washington, D.C.