NEW YORK — (CNN) The race to become the liberal alternative to Hillary Clinton is on.

Thanks to a new poll, which shows Clinton has some serious vulnerabilities when it comes to trustworthiness and likeability, contenders like Vermont’s Bernie Sanders and Maryland’s Martin O’Malley may have more room to make their case than previously thought.

A more alarming sign for Clinton: Prospective Republican opponents have closed on her in head-to-head matchups, with Kentucky Sen. Rand Paul, Florida Sen. Marco Rubio and Wisconsin Gov. Scott Walker all now polling within the margin of error.

Clinton’s favorability rating is now 46% — down from 53% in March. And just 42% said they view Clinton as honest and trustworthy, compared to 50% in March, according to a new CNN/ORC poll.

The greatest threat to her chances of securing the Democratic nomination — the potential for a Sen. Elizabeth Warren candidacy — is apparently over. But the polling shows she’ll still have to come to play against the likes of liberal folk hero Sanders and the willing-to-throw-a-punch O’Malley.

Clinton’s share of Democrats’ support has slipped from 69% in April to 60% six weeks later. Second, though, is Vice President Joe Biden, at 14%. Sanders is at 10%, double his support from March, while O’Malley still barely registers at 1%.

The former Maryland governor officially launched his campaign over the weekend, and Sanders made news by attracting crowds of hundreds to events on his first swing through Iowa.

“That was an indication of the fact that Iowa voters definitely want to get engaged,” said Tom Henderson, the Democratic chairman in Polk County, Iowa’s most populous county.

Though there are apparent cracks in the armor, top Democratic hands say Clinton is still on safe territory.

“If either one of them were to win, it would be the greatest upset in the history of politics,” said Dan Pfeiffer, a CNN political commentator and former senior White House aide to President Barack Obama.

And Clinton’s campaign is making as clear as it can that the former secretary of state is preparing for a real primary battle — particularly in early-voting states like Iowa.

On June 13 — the same day Clinton holds her first major speech and rally of the campaign in New York City — she’ll meet with key supporters and volunteers in the Hawkeye State, and simulcast that meeting to similar ones in nearly all 435 congressional districts across the country.

In the 2008 campaign, Clinton was stunned by a third-place finish behind Barack Obama and Sen. John Edwards. It’s a lesson that seems to have been taken to heart for her 2012 campaign.

Team Clinton already employs 21 field organizers and six regional organizing directors in Iowa, and those organizers are working down to the precinct level. The staff includes state director Matt Paul and deputy state director Molly Schermann, who both worked for former Iowa governor and Agriculture Secretary Tom Vilsack, as well as political director Troy Price, the former executive director of the Iowa Democratic Party.

That said, her advisers know Iowa has always been a game of expectations, and they are doing their best to temper them.

Clinton campaign spokesman Jesse Ferguson on Monday highlighted a number many Clinton allies have cited: No Democrat who wasn’t a sitting president, vice president or Iowa senator has ever topped 50% of the state’s caucus vote.

Still, Clinton is far from a typical candidate.

Henderson, the Polk County Democratic chair, said it’s unfair to compare low-profile candidates like Sanders and O’Malley with Clinton.

“We keep comparing these candidates to Hillary Clinton, who may be the most famous women in the world, and a lot of them are still emerging — people are getting to know them,” he said. “It’s still early in the campaign.”

The biggest danger to Clinton’s candidacy is the emergence of a damaging narrative — that she acts like she’s above reproach when it comes to questions over her use of private email while heading the State Department or the controversial donations accepted by the Clinton Foundation. Or that she’s completely untrustworthy.

She’s faced criticism in recent weeks for closed off campaign — seldom fielding questions from reporters, and when she does, ending those question-and-answer sessions in a matter of minutes.

Republicans, meanwhile, have sought to capitalize on the growing seeds of distrust, accusing Clinton of corruption and unacceptable secrecy, pointing to her tightly scripted campaign events and refusal to answer inquiries about Benghazi, her emails or her family’s foundation.

“Those are legitimate questions, and she’s going to have to address all of those and a lot more over the course of this campaign. She’s probably going to have to do it sooner rather than later,” Pfeiffer told CNN’s Jake Tapper on “The Lead” Monday.

“If she doesn’t answer those questions, it will hurt her in the long run,” he said.

The-CNN-Wire ™ & © 2015 Cable News Network, Inc., a Time Warner Company. All rights reserved. (PHOTO: Barbara Kinney/Hillary Clinton/Facebook)