Washington (CNN) More people have an unfavorable view of Democratic front-runner Hillary Clinton now than at any time since 2001, according to a new CNN/ORC poll on the 2016 race.

While Clinton remains strikingly dominant in the Democratic field, the poll shows that her numbers have dropped significantly across several key indicators since she launched her campaign in April.

A growing number of people say she is not honest and trustworthy (57%, up from 49% in March), less than half feel she cares about people like them (47%, down from 53% last July) and more now feel she does not inspire confidence (50%, up from 42% last March).

In head-to-head match-ups against top Republicans, her margin is tighter than it has been at any point in CNN/ORC's polling on the contest.

Pfeiffer: Clinton is going to have to engage the press

Pfeiffer: Clinton is going to have to engage the press 05:02

Pfeiffer: Clinton is going to have to engage the press

On the Republican side, though, no candidate has successfully broken out of the pack.

Much of Clinton's fade is attributable to shifts among independents, but she's also losing some ground among her own partisans. Her support in the Democratic nomination contest has dropped 9 points since April, and though more than 8-in-10 Democrats said they thought she was honest and trustworthy earlier this year; now, just 73% say so.

The new CNN/ORC poll looking at the shape of the race for the presidency in 2016 finds these warning signs for Clinton, alongside some concerns for the Republican Party's best-known contender, Jeb Bush.

Jeb Bush's family ties

Bush's efforts to separate himself from his brother have worked to some extent. Only about half of Americans say Bush is "a lot like his brother."

But most -- 56% -- say his connection to two former presidents would make them less likely to back him for the presidency. Just 27% say that connection would make them more likely to back the former Florida governor.

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That's virtually the opposite situation of what his brother faced when George W. Bush made his initial run for the presidency in 1999. Back then, 42% said Bush's connection to his father made them more likely to back him, while only 24% said it was a deterrent.

Bush's family ties are slightly more of a draw for Republicans, but not by much. Among Republicans and Republican-leaning independents, 42% say they're more likely to back Jeb Bush because of his connections, while 38% say they are less likely to vote for him because of that.

No leader emerges in the GOP pack

For the bulk of the GOP field, however, the race for the Republican nomination remains an effort to distinguish themselves from the pack and no one has yet succeeded at that.

Though there has been some shuffling at the top of the GOP order since the last CNN/ORC poll in April, no individual candidate's movement lies outside of the margin of sampling error.

Rubio tops the field with 14%, with Bush near even at 13%. Huckabee and Walker follow at 10% each, with Cruz (8%), Paul (8%) and Carson (7%) all within striking distance of double-digit support.

Paul prompts the largest gender gap on the GOP side, drawing 13% and tying for first among men while garnering just 2% support among women.

The top of the field is similar among conservative Republicans to the overall horse race numbers, but among those who consider themselves tea party supporters, there's a clear leader: Scott Walker with 19% support. His closest competitor is Ted Cruz with 12%.

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Overall, about half of Republicans (49%) would like to see the field resolve early, saying it would be best for the party if one strong candidate emerged early as a clear frontrunner. But 46% say they would prefer a longer campaign, with a number of strong contenders competing over the next year.

One possible differentiator emerges: The poll finds a distinct difference in which candidates Republicans view as representing the future rather than the past.

Three-quarters of Republicans describe Marco Rubio (77%) or Scott Walker (75%) as representing the future, nearly 7-in-10 say so about Rand Paul (68%), but Bush (51%) and Christie (51%) are far less likely to be seen as representative of the future.

The growing Democratic field

Democrats are more likely than Republicans to say they would like a competitive primary (53% say that would be best for the party), but their preferences so far don't portend a close contest.

Clinton continues to hold a massive lead in that race, with 60% of Democrats saying she would be their top choice for the nomination. Behind her, 14% would favor Vice President Joe Biden, and 10% prefer Vermont Sen. Bernie Sanders.

Martin O'Malley, the former Maryland governor who announced his candidacy on Saturday, barely registers with 1% support.

Sanders does fare better among liberals than overall, carrying 18% support among that group, but Clinton still notches 61% among the liberals in her party.

Getting closer to the general

In general election match-ups, Clinton now runs about even with Rand Paul, Scott Walker and Marco Rubio, while she continues to top Bush and Ted Cruz by a significant margin.

As noted above, those shifts stem largely from a change among independents, though Republicans appear to be solidifying their support for GOP candidates while Democrats are slightly less certain about Clinton.

One feature of the race that has held even as the numbers shifted: These match-ups prompt enormous gender gaps. According to the poll, the gender gaps remain over 20 points in each of the five match-ups tested, including a whopping 34-point gender gap in Clinton's match-up with Scott Walker.

Her declining support in those general election match-ups, alongside falling favorability ratings and worsening impressions of her, suggests recent news about her actions as secretary of state may have taken a toll.

Photos: Potential 2016 presidential candidates Former Florida Gov. Jeb Bush has said his decision to run for the Republican nomination will be based on two things: his family and whether he can lift America's spirit. His father and brother are former Presidents. Hide Caption 1 of 19 Photos: Potential 2016 presidential candidates Wisconsin Gov. Scott Walker has created a political committee that will help him travel and raise money while he considers a 2016 bid. Additionally, billionaire businessman David Koch said in a private gathering in Manhattan this month that he wants Walker to be the next president, but he doesn't plan to back anyone in the primaries. Hide Caption 2 of 19 Photos: Potential 2016 presidential candidates Louisiana Gov. Bobby Jindal is establishing a committee to formally explore a White House bid. "If I run, my candidacy will be based on the idea that the American people are ready to try a dramatically different direction," he said in a news release provided to CNN on Monday, May 18 Hide Caption 3 of 19 Photos: Potential 2016 presidential candidates Sen. Bernie Sanders , an independent from Vermont who caucuses with Democrats, has said the United States needs a "political revolution" of working-class Americans looking to take back control of the government from billionaires. He first announced the run in an email to supporters early on the morning of Thursday, April 30. Hide Caption 4 of 19 Photos: Potential 2016 presidential candidates On March 2, retired neurosurgeon Ben Carson announced the launch of an exploratory committee. The move will allow him to raise money that could eventually be transferred to an official presidential campaign and indicates he is on track with stated plans to formally announce a bid in May. Hide Caption 5 of 19 Photos: Potential 2016 presidential candidates South Carolina Sen. Lindsey Graham has said he'll make a decision about a presidential run sometime soon. A potential bid could focus on Graham's foreign policy stance. Hide Caption 6 of 19 Photos: Potential 2016 presidential candidates Hillary Clinton launched her presidential bid Sunday, April 12, through a video message on social media. She continues to be considered the overwhelming front-runner among possible 2016 Democratic presidential candidates. Hide Caption 7 of 19 Photos: Potential 2016 presidential candidates Sen. Marco Rubio announced his bid for the 2016 presidency on Monday, April 13, a day after Hillary Clinton, with a rally in Florida. He's a Republican rising star from Florida who swept into office in 2010 on the back of tea party fervor. But his support of comprehensive immigration reform, which passed the Senate but has stalled in the House, has led some in his party to sour on his prospects. Hide Caption 8 of 19 Photos: Potential 2016 presidential candidates Lincoln Chafee, a Republican-turned-independent-turned-Democrat former governor and senator of Rhode Island, said he's running for president on Thursday, April 16, as a Democrat, but his spokeswoman said the campaign is still in the presidential exploratory committee stages. Hide Caption 9 of 19 Photos: Potential 2016 presidential candidates Jim Webb, the former Democratic senator from Virginia, is entertaining a 2016 presidential run. In January, he told NPR that his party has not focused on white, working-class voters in past elections. Hide Caption 10 of 19 Photos: Potential 2016 presidential candidates Vice President Joe Biden has twice before made unsuccessful bids for the Oval Office -- in 1988 and 2008. A former senator known for his foreign policy and national security expertise, Biden made the rounds on the morning shows recently and said he thinks he'd "make a good President." Hide Caption 11 of 19 Photos: Potential 2016 presidential candidates New Jersey Gov. Chris Christie has started a series of town halls in New Hampshire to test the presidential waters, becoming more comfortable talking about national issues and staking out positions on hot topic debates. Hide Caption 12 of 19 Photos: Potential 2016 presidential candidates Rep. Paul Ryan, a former 2012 vice presidential candidate and fiscally conservative budget hawk, says he's keeping his "options open" for a possible presidential run but is not focused on it. Hide Caption 13 of 19 Photos: Potential 2016 presidential candidates Sen. Rand Paul officially announced his presidential bid on Tuesday, April 7, at a rally in Louisville, Kentucky. The tea party favorite probably will have to address previous controversies that include comments on civil rights, a plagiarism allegation and his assertion that the top NSA official lied to Congress about surveillance. Hide Caption 14 of 19 Photos: Potential 2016 presidential candidates Texas Sen. Ted Cruz announced his 2016 presidential bid on Monday, March 23, in a speech at Liberty University. The first-term Republican and tea party darling is considered a gifted orator and smart politician. He is best known in the Senate for his marathon filibuster over defunding Obamacare. Hide Caption 15 of 19 Photos: Potential 2016 presidential candidates Democrat Martin O'Malley, the former Maryland governor, released a "buzzy" political video in November 2013 in tandem with visits to New Hampshire. He also headlined a Democratic Party event in South Carolina, which holds the first Southern primary. Hide Caption 16 of 19 Photos: Potential 2016 presidential candidates Republican Rick Perry, the former Texas governor, announced in 2013 that he would not be seeking re-election, leading to speculation that he might mount a second White House bid. Hide Caption 17 of 19 Photos: Potential 2016 presidential candidates Former Pennsylvania Sen. Rick Santorum, a social conservative, gave Mitt Romney his toughest challenge in the nomination fight last time out and has made trips recently to early voting states, including Iowa and South Carolina. Hide Caption 18 of 19 Photos: Potential 2016 presidential candidates Political observers expect New York Gov. Andrew Cuomo to yield to Hillary Clinton's run in 2016, fearing there wouldn't be room in the race for two Democrats from the Empire State. Hide Caption 19 of 19

Though most -- 61% -- think the release of Clinton's emails over the next months from her time as secretary of state will not reveal any previously hidden wrongdoing, the poll also finds 58% are dissatisfied with the way she handled the attack in Benghazi in 2012.

A narrow majority feel the Republican-led congressional hearings on the attack have been handled appropriately, just 41% say the GOP has gone too far with them.

Clinton's family ties to a president are more of a wash than Bush's. While 39% say her marriage to Bill Clinton makes them more likely to vote for her, the same share say it's a turn-off. And most Americans say Clinton is not like her husband at all (54%).

The CNN/ORC Poll was conducted by telephone May 29-31, among a random national sample of 1,025 adults. The margin of sampling error for results among the full sample is plus or minus 3 percentage points. It is 4.5 points for results among the 433 Democrats and Democratic-leaning independents and the 483 Republicans and Republican-leaning independents.