Hillary Rodham Clinton has been the favorite for the Democratic presidential nomination for several years, and in recent months the only unanswered question has been when she would announce her candidacy.

Now, an equally important question appears to be: How long will it take for concerns about her use of a private server for e-mails to blow over?

A new poll from Quinnipiac University suggests that public mistrust continues to linger. In the meantime, a number of new Republican challengers have begun to edge ahead of her in key swing states, the poll says – a fact that could accelerate her campaign announcement.

The poll, released Thursday, shows Mrs. Clinton falling narrowly behind Sen. Rand Paul (R) of Kentucky in Iowa, and by three points in Colorado. She is effectively tied with every Republican candidate in Colorado, according to the poll, and has a narrow lead over most GOP candidates in Iowa, with the exception of Senator Paul.

Peter Brown, assistant director of the Quinnipiac University Poll, said in a statement that the results are "a boost" for Paul, who officially launched his 2016 presidential campaign earlier this week.

The one positive in the poll for Clinton is that she leads all Republican candidates in Virginia – the largest of the three swing states polled – including a four point lead over Paul.

But it's still early in the 2016 presidential cycle and polls are often volatile. In March 2014, Clinton led Paul by 10 points in a hypothetical Hawkeye State matchup, according to a Quinnipiac poll. At that time, her lead against other GOP prospects in Iowa was even stronger: Clinton was up 16 points against Sen. Ted Cruz of Texas, 14 points against former Gov. Jeb Bush of Florida, and 13 points against Gov. Chris Christie of New Jersey.

Since mid-February, Clinton has lost ground in almost every matchup in Colorado and Iowa, according to a Quinnipiac poll released Feb. 18. Her closest challenger in Iowa in February was former Arkansas Gov. Mike Huckabee, and he trailed Clinton then by seven points, 45 percent to 38 percent. Now they are tied at 42 percent.

"Ominous for Hillary Clinton is the broad scope of the movement today compared to her showing in Quinnipiac University's mid-February survey," said Mr. Brown. "It isn't just one or two Republicans who are stepping up; it's virtually the entire GOP field that is running better against her."

So far, Paul and Senator Cruz are the only Republicans to have formally announced their 2016 candidacy. Other GOP contenders are expected to include Sen. Marco Rubio of Florida, Gov. Scott Walker of Wisconsin, as well as Governors Christie, Bush, and Huckabee.

The majority of respondents in each of the three swing states said they do not think Clinton is honest and trustworthy, though a majority of respondents said they think she has strong leadership qualities, and that they approved of the way she handled her job as secretary of State.

"It is difficult to see Secretary Clinton's slippage as anything other than a further toll on her image from the furor over her e-mail," said Brown. "Voters do think she is a strong leader – a key metric – but unless she can change the honesty perception, running as a competent but dishonest candidate has serious potential problems."

Just a few months ago, it appeared that Clinton was in no rush to formally announce her campaign, happy instead to stay on the sidelines raising money. Back in December, her biggest concern was waiting too long and potentially having her campaign thunder stolen by left-wing firebrand Sen. Elizabeth Warren (D) of Massachusetts.

Senator Warren still says that she is not planning to enter the race in 2016, but in the wake of the e-mail scandal last month Democratic strategists urged Clinton to launch her campaign early.

"The whole situation underscores the need for her to announce her candidacy, as an actual campaign would be the best way to deal with issues like this if they come up," said Kathy Winter, chairwoman of Iowa’s Osceola County Democrats, in an interview with Politico.

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In the meantime, the growing field of Republican presidential hopefuls are reaping the benefits of the scandal.

"The e-mail controversy is opening doors to candidates who had little traction as Hillary Clinton gets bad numbers on trust and honesty," said Tim Malloy, assistant director of the Quinnipiac University Poll.