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Senator Marco Rubio of Florida at a Republican convention in Georgia last week. His Cuban heritage and his youth are expected to help him gain voter support.CreditDavid Goldman/Associated Press 
WASHINGTON — They use words like “historic” and “charismatic,” phrases like “great potential” and “million-dollar smile.” They notice audience members moved to tears by an American-dream-come-true success story. When they look at the cold, hard political math, they get uneasy.
An incipient sense of anxiety is tugging at some Democrats — a feeling tersely captured in four words from a blog post written recently by a seasoned party strategist in Florida: “Marco Rubio scares me.”
What is so unnerving to them at this early phase of the 2016 presidential campaign still seems, at worst, a distant danger: the prospect of a head-to-head general-election contest between Mr. Rubio, the Republican senator from Florida, and Hillary Rodham Clinton.
Yet the worriers include some on Mrs. Clinton’s team. And even former President Bill Clinton is said to worry that Mr. Rubio could become the Republican nominee, whittle away at Mrs. Clinton’s support from Hispanics and jeopardize her chances of carrying Florida’s vital 29 electoral votes.
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What Marco Rubio Would Need to Do to Win 

Democrats express concerns not only about whether Mr. Rubio, 43, a son of Cuban immigrants, will win over Hispanic voters, a growing and increasingly important slice of the electorate. They also worry that he would offer a sharp generational contrast to Mrs. Clinton, a fixture in American politics for nearly a quarter-century who will turn 69 before the election.
As her supporters recall, Barack Obama beat Mrs. Clinton for the nomination in the 2008 elections after drawing similar contrasts himself.
Patti Solis Doyle, who ran Mrs. Clinton’s presidential campaign for most of the 2008 contest, said Mr. Rubio “could have the ability to nip away at the numbers for the Democrats.”
Ms. Doyle, the first Hispanic woman to manage a presidential campaign, added that Mr. Rubio could allow Republicans to regain a “reasonable percentage” of the Hispanic vote. In 2012, just 27 percent of Hispanics voted for the Republican candidate, Mitt Romney.
Mr. Rubio “is a powerful speaker,” Ms. Doyle added. “He is young. He is very motivational. He has a powerful story.”
Recognizing how essential it is to win Hispanic support, Mrs. Clinton has gone further in laying out an immigration policy than she has on almost any other issue, saying that she would extend greater protections to halt deportations of people in the United States illegally. She has also hired a former undocumented immigrant to lead her Latino outreach efforts.
Her own strategists, their allies in the “super PACs” working on her behalf and the Democratic Party all say they see plenty of vulnerabilities in Mr. Rubio’s record and his views. And they are trying to shape the perception people have of him while polls show that he is still relatively unknown: Yes, the Democratic National Committee said in a recent memo, Mr. Rubio was a fresh face, but one “peddling a tired playbook of policies that endanger our country, hurt the middle class, and stifle the American dream.”
So far, Democrats who have combed over Mr. Rubio’s voting record in the Senate have seized on his opposition to legislation raising the minimum wage and to expanding college loan refinancing, trying to cast him as no different from other Republicans.
The subtext: He may be Hispanic, but he is not on the side of Hispanics when it comes to the issues they care about.
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What Hillary Clinton Would Need to Do to Win 

Democrats will try to use Mr. Rubio’s youth and four-year career in national politics against him, depicting him as green or naïve — a liability at a time when unrest abroad is a top concern. “A Dan Quayle without the experience,” suggested Christopher Lehane, a veteran strategist who has worked for the Clintons.
Bill Richardson, the former governor of New Mexico, who is of Mexican heritage, said Democrats would also make an issue of Mr. Rubio’s mixed record on how to overhaul the immigration system: He initially supported a Senate bill to grant people in the United States illegally a path to citizenship, but he later backed down.
Mr. Richardson said that would poison his chances with Hispanic voters. “His own Hispanic potential would defeat him,” he said.
It is also unclear how much Mr. Rubio would appeal to Puerto Ricans, Mexicans and other voters with Latin American ancestry who may not feel much cultural affinity with a Cuban-American.
Still, when many Democrats assess Mr. Rubio’s chances, as nearly a dozen of them did for this article, they put him in the top tier of potential candidates who concern them the most, along with former Gov. Jeb Bush, another Floridian who is courting Hispanics, and Gov. Scott Walker of Wisconsin.
Mr. Rubio’s heritage and his youth could be particularly dangerous to Mrs. Clinton, they said. Each of those points could help neutralize one of her biggest strengths: the opportunity to help elect the first female president, and the experience Mrs. Clinton gained as secretary of state.
Mr. Rubio already appears to be pursuing that strategy. By calling himself a candidate of the “21st century, not the 20th,” he seeks both to turn Mrs. Clinton’s long career against her and to entice voters who may desire a change of direction.
In Florida, Democrats who have watched Mr. Rubio’s rise warn against playing down his strengths.
Former Gov. Charlie Crist, who lost to Mr. Rubio in a 2010 Senate race after dropping his Republican Party affiliation, said he admired how Mr. Rubio told the story of his immigrant parents — his mother a maid, his father a bartender — and how they worked hard so that he could succeed. “It’s hard to get more compelling than that,” Mr. Crist said.
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John Morgan, a major Democratic donor in Florida who will hold a fund-raiser for Mrs. Clinton next week, said he planned to raise the issue of Mr. Rubio’s strengths with her.
“Jim Messina talks about how elections are about where we want to go from here,” Mr. Morgan said, naming the strategist who helped President Obama win two national elections. What is problematic about Mr. Rubio, he said, is “his theme will be, ‘We don’t want to go back; we need to go forward.’ ”
“I think they do underestimate him,” Mr. Morgan added. “He’s energetic, he’s photogenic, and he will say whatever you want him to say.”
Steve Schale, the Florida strategist who wrote the “Marco Rubio scares me” blog post, said that when he worked for the Democratic leader of the Florida House of Representatives, his boss, Dan Gelber, had a saying about Mr. Rubio’s effect on crowds, and about his sincerity: “Young women swoon, old women pass out, and toilets flush themselves.”
And Mr. Gelber himself recalled the day in Tallahassee, Fla., in 2008 when he and Mr. Rubio, then the speaker of the State House, gave their farewell speeches. He spoke first, followed by Mr. Rubio, as Mr. Gelber’s wife looked on.
“She’s sitting there weeping,” Mr. Gelber recalled, still incredulous. “And I look up, and I mouth, ‘Are you kidding me?’ ”
Mr. Gelber praised Mr. Rubio’s ability to use his family’s story to convey compassion for people marginalized by society, but he said he believed, as many Democrats do, that this was disingenuous.
“It’s a little maddening when his policies are so inconsistent with that,” Mr. Gelber said. “My head would explode.”
A Rubio-Clinton contest could ultimately come down to Florida. Republicans can ill afford to lose the state if they hope to win the White House. And bleeding Hispanic votes could make Mrs. Clinton’s path much harder.
“Losing a point among whites means winning Hispanics by about 5 percent more just to make up that loss,” Mr. Schale wrote in his memo on Florida’s election demographics. If Democrats continue to lose white voters, he added, Mr. Rubio’s place on the ballot would only complicate matters.
“He should be the one you don’t want to face,” Mr. Schale wrote.
Correction: May 22, 2015 
An earlier version of this article referred incorrectly to former Gov. Charlie Crist’s loss in the 2010 United States Senate race in Florida. Mr. Crist lost to Marco Rubio in the general election, not in the Republican primary.