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“The Boko Haram leader, or whoever Boko Haram had perform on video, is a good-looking guy. This is why Mrs. Clinton wouldn’t call this terror group a terror group, because they’re black,” Mr. Limbaugh said on his radio show Monday, according to a transcript. “Can’t afford to do this. This is how surface-conscious the left is.”

The Obama factor

Political analysts say most voters already have formed opinions about Mrs. Clinton from her eight years as first lady, eight years as U.S. senator from New York and four years as secretary of state.

Still, Mrs. Clinton’s unbreakable ties to Mr. Obama could be the deciding factor on how some Americans cast ballots.

“A lot depends not on Clinton herself but on Barack Obama and how much she will feel the need to escape Barack Obama’s shadow in 2016,” said Dante Scala, a political science professor at the University of New Hampshire who tracks presidential politics. “Perhaps the answer will be she will need to do that, and perhaps her own high public profile will come in handy. Maybe she’ll see ample reason to not run for Barack Obama’s third term.”

Analysts say Mrs. Clinton would have a difficult challenge if she tries to change minds and win support for ambitious policy proposals. Instead, they say, Americans may decide whether she is presidential material based on what she has and hasn’t done or has and hasn’t said over the past two decades.

“She’s been in the spotlight since 1991 nationally. It will have been 25 years of a very, very public persona. Even if there had been candidates who had been this well-known, in this digital age, with the way the news works now, she’s the focus of so many stories, she’s on so many home pages. It’s impossible not to track her, to follow her,” said Jennifer Lawless, director of the Women and Politics Institute at American University in Washington.

Ms. Lawless said that presents both challenges and advantages.

“She faces a difficult set of circumstances in that people already have pretty strong feelings about her. But the upside of that is the additional stuff that Republicans throw at the wall about her likely won’t have a big impact either,” she said.

“If people’s predispositions are so formed, the campaign will matter a little bit. But there’s not going to be a lot of new information that people factor into their assessments.”

Other analysts say some voters may ignore Mrs. Clinton’s past altogether and give her a chance to lay out her vision for the future.

“I think they would be open to a Clinton candidacy. I think she’s lost some of her polarizing edge, though I’m sure some of that is going to come back,” Mr. Scala said. “At this point, I think they’re at least willing to listen to what she has to say.”