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– Republican Marco Rubio and Democrat Hillary Clinton are early favorites among Minnesota voters in the presidential race, according to a new Star Tribune poll.

Clinton holds a commanding 34-point lead over rival Vermont Sen. Bernie Sanders, but the statewide poll of 800 registered voters shows that the former secretary of state could face trouble against two top Republicans. In head-to-head matchups, Clinton is essentially tied with Texas Sen. Ted Cruz and trails Rubio, the Florida U.S. senator. Clinton tops Donald Trump by 5 percentage points.

Minnesota GOP voters appear deeply divided, with Rubio’s lead within the poll’s margin of sampling error. Cruz and New York developer Donald Trump are each capturing a sizable share of voters. Retired neurosurgeon Ben Carson, former Florida Gov. Jeb Bush and New Jersey Gov. Chris Christie trail further behind.

The poll showing Clinton’s apparent challenges in Minnesota against Republicans comes as Sanders appears to be surging in Iowa, where voters will caucus Feb. 1, the first in the nation to do so. On Tuesday, Sanders will visit Duluth and St. Paul as he works to build his Minnesota support.

Finding a Democratic candidate who can beat Republicans is foremost on the mind of Debby Ortman, of Hermantown, Minn. Ortman, a “die-hard” liberal who is more progressive than Clinton, nevertheless believes “Hillary has a better chance of taking on Republicans.”

But in a hypothetical matchup between Clinton and Rubio, Clinton trails the Florida senator by nine points, 40 to 49, with 11 percent undecided. In a matchup between Clinton and Cruz, the poll showed her trailing by two points, with 12 percent undecided.

The poll has a margin of sampling error of plus or minus 3.5 percentage points.

The Star Tribune poll is among the first to show Rubio leading the GOP race in a state. Recent Iowa surveys show Trump and Cruz vying for first place. Trump has a large lead in New Hampshire, polls show.

“A lot of people are looking at Rubio right now to see if he emerges,” said Joseph Peschek, a political scientist at Hamline University in St. Paul. “A lot of Republican voters aren’t sure who to support, and I think they will be watching Iowa and New Hampshire and the early contests to see who shakes out.”

The poll suggests that Rubio has wide appeal among Republicans seeking an alternative to Trump and Cruz who could win over independents in the general election.

“In Minnesota, we have libertarians, social conservatives and fiscal conservatives. He strikes me as that big-tent Republican who can bring people together,” said Jen Niska, an Anoka County mother and Rubio backer. “He’s conservative … and he’s approachable and nice.”

Rubio had the highest favorable name recognition among the GOP field in the poll, at 38 percent. Bush and Trump had the highest unfavorable name recognition at 61 percent each. The number of Minnesotans who have an unfavorable view of Clinton is much higher, at 52 percent, than who share the same view of Rubio, although 21 percent of respondents had yet to form an opinion of him.

The poll also shows that a large number voters — particularly independents — are still undecided.

Rubio appears to have an advantage in appealing to independent Minnesota voters, who could prove crucial in the general election. Independents break 54 percent for Rubio and 30 percent for Clinton in a head-to-head matchup.

Some Minnesota voters showed interest in candidates who have proved to be more nontraditional.

Dan Mohr, a Ramsey resident, said he can’t decide between Sanders and Trump, adding that he prefers an outsider. “They’re outside the norm and we need someone to get something done,” he said.

Clinton’s biggest challenge in the state appears to be firming up support outside the Twin Cities.

In Hennepin and Ramsey counties, she trounces Rubio 52 percent to 37 percent. Outside the Twin Cities and surrounding suburbs, Clinton’s support falls to 30 percent in a Rubio matchup.

Among female voters, Clinton holds a strong lead over Cruz and particularly Trump, beating him by 22 points. But Rubio essentially pulls even with Clinton among women, trailing 44 percent to 45 percent.

Republican officials said they expect the GOP race to change as candidates begin dropping out and voters start paying closer attention.

“Large numbers of Americans tune out of these contests at this stage, they think it’s just way too early,” said state GOP Chairman Keith Downey. “Undecideds always narrow as the pool of candidates shrink.”

Downey said the positive results for Rubio and Cruz statewide are encouraging.

“That we have candidates who are doing well against Hillary speaks well,” he said.

DFL Party Chairman Ken Martin said he is not worried that Republicans are topping Clinton in the poll. He said Clinton and Sanders are still locked in a battle for the party’s nomination, which takes the focus away from GOP rivals. He noted that Minnesota has backed the Democratic presidential candidate dating back to 1976.

“Neither field is set right now,” Martin said. “Is it worrisome to me at all? No. It’s early.”

Minnesota’s party caucuses are March 1, a date shared with 14 other states that either caucus or hold primaries. The caucuses usually draw the party faithful — this year about 60,000 Minnesotans are expected to participate — but the winners usually don’t reflect the sentiments of the broader voting population.

In 2012, Minnesota Republicans selected Rick Santorum in the caucus. He went on to lose the party nomination to Mitt Romney. In the new poll, Santorum, who is running again, was favored by just 1 percent of Minnesota voters.

Judy Hoover of Golden Valley is leaning toward supporting a Democrat, but hasn’t decided between Sanders and Clinton. She is drawn to Sanders’ push for universal health care and curbing income inequality, but she thinks Clinton would be more electable and likable.

“Bernie comes across as being too radical and harsh. With Clinton, she is smoother,” Hoover said. “I would trust her much more with international affairs and she’s had more experience.”

Allison Sherry • 202-383-6120