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MIAMI (CBSMiami) — Ahead of the Florida primary, the Donald Trump machine rolls into the state with a big lead over native son Sen. Marco Rubio, according to an independent Quinnipiac University poll released Thursday.

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Polling shows Trump with a commanding lead over Rubio, 44-28 percent, among Florida’s Republican primary voters.

Texas Sen. Ted Cruz got 12 percent, Ohio Gov. John Kasich sits at seven percent and Dr. Ben Carson trails the pack at four percent. Another six percent are undecided.

Among the genders, Trump leads with both men (49-25 percent) and women (39-31 percent) over Rubio.

“This is a devastating poll for Marco Rubio,” said political pollster and analyst Fernand Amandi of the firm Bendixen and Amandi. “If he cannot win his home state of Florida he needs to face the fact theat he’s probably out of these GOP sweepstakes for the Presidency.”

“We’re going to win Florida,” said an upbeat Ana Carbonell, a front person for the Rubio campaign in Florida at her office in Coral Gables.

Carbonell said with 19 days remaining, there is plenty of time for Rubio to plow lost ground and overcome Trump’s seeming advantage.

“We have no doubt that when the votes are counted, Marco Rubio will win Florida and the 99 delegates that come with it,” Carbonell said.

At a cafecito window in Doral, Rubio supporter Lourdes Blanco was bowled over by the poll numbers – sort of.

“Wow, that’s crazy, that’s crazy,” Blanco said, but then expanded on her reaction.

“I’m not surprised,” she said. “I’m not surprised.”

She was not surprised because of the so-called “Trump factor.”

Despite an unorthodox, and to some offensive style, Trump continues to tear up the GOP field.

“This is a phenomenon,” said Amandi.  “It has upended all the political pundits and analysts.”

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Twenty one percent of the primary voters polled by Quinnipiac say they “would definitely not support” Trump for the nomination, compared to 17 percent for Rubio.

Trump’s remarks have often been over the top in terms of traditional presidential candidates.

In touting those who supported him in the Nevada caucuses, for instance, Trump said, “We won the uneducated poor. I love the uneducated poor!”

In Nevada on Wednesday, Rubio seemed to try to take advantage of Trump’s rhetoric, without mentioning him by name.

“I never want you to watch me on TV and cringe, and say, ‘I can’t believe I supported him,’” Rubio said, as the crowd cheered.

Strong leadership was the most important quality in a candidate for president, 32 percent of Florida Republicans said.

“A third of likely primary voters say a candidate who is a strong leader is key to their choice and 66 percent of them support Trump,” said Peter A. Brown, assistant director of the Quinnipiac University Poll.

Trump is the choice for 66 percent of the likely Republican primary voters who most want a candidate with strong leadership. Rubio only saw 16 percent, though they are tied 30 – 30 percent among those who said they want a candidate who is honest and trustworthy.

“The size and shape of Trump’s lead is impressive. He leads in every age group by nine to 19 percentage points. He does better among men than among women and, despite being a New York multi-billionaire, he leads among those who identify with the Tea Party,” Brown added.

The economy was considered the biggest issue this election, according to 31 percent of those polled. Trump tops Rubio 51-28 percent among those voters. Terrorism was listed as the second biggest issue at 18 percent, followed by immigration at 14 percent.

Always a swing state, Florida is primed to be the biggest battle ground state in the country this election.

“Florida is the single biggest prize of the primary season because it is the largest state to allocate its delegates on a winner-take-all basis. If Sen. Rubio can’t win in his own home state, it is difficult to see how he can win elsewhere,” said Brown.

Florida election law could add to more uncertainty than primaries already counted in other states.

“Only registered Republicans may vote here, which raises the question of whether the flood of new voters Donald Trump seemed to bring to earlier contests will be able to participate in Florida,” Brown said.

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From February 21-24, Quinnipiac University surveyed 705 Florida likely Republican primary voters with a margin of error of +/- 3.7 percentage points. Live interviewers call land lines and cell phones.