Iowa City, Iowa (CNN) In Hillary Clinton 's first national interview of the 2016 race, she attacked her Republican rivals on immigration and dismissed the suggestion that the American people have a problem trusting her.

"People should and do trust me," she told CNN's Brianna Keilar.

She blamed the "barrage of attacks that are largely fomented by and coming from the right" for fueling a perception that trust is an area of vulnerability for her.

Clinton displayed little hesitation about attacking Republicans herself, saying that she is "very disappointed" in Donald Trump for his comments about immigrants and in the Republican Party for not condemning his remarks more quickly.

She then pivoted to skewering the entire GOP field for their immigration stance, saying, "They're on a spectrum of hostility, which I think is really regrettable in a nation of immigrants like ours."

The interview foreshadowed the Clinton that will hit the campaign trail in the coming months as election season heats up. She was occasionally defensive, especially when pressed on whether she has any responsibility for the public's mistrust in her. But she had no problem with going on the offense against her Republican challengers.

Clinton took direct aim at GOP rival Jeb Bush.

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"He doesn't believe in a path to citizenship. If he did at one time, he no longer does," she said.

The Bush campaign rebuffed Clinton's criticism and instead accused her of flip-flopping on immigration.

"Hillary Clinton will say anything to get elected and her numerous flip-flops on immigration prove it," said Emily Benavides, a Bush campaign spokeswoman, in a statement.

"As he outlined in his book on this issue, Gov. Bush believes in a conservative legislative solution to fix our broken immigration system that includes earned legal status for those currently in the country after they pay fines and taxes, learn English and commit no substantial crimes while securing our border," she said.

Clinton also blamed the city of San Francisco for mishandling the case of an undocumented immigrant who had been deported five times before killing a woman there -- in a sanctuary city where local law enforcement do not enforce federal immigration laws.

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"The city made a mistake, not to deport someone that the federal government strongly felt should be deported," she said. "I have absolutely no support for a city that ignores the strong evidence that should be acted on."

The full interview aired Tuesday on "The Situation Room with Wolf Blitzer" and will re-air at 8 p.m. on "Anderson Cooper 360."

Pressed on why the public has a hard time trusting her, Clinton maintained she faced "the same kind of onslaught" in her two New York Senate campaigns and her confirmation as secretary of state, and said Republicans have sought to turn controversies like her use of a private email address and the Clinton Foundation's actions against her.

And that, Clinton said, is why national polls and swing-state surveys have found that a majority of voters say they don't see her as honest and trustworthy.

A Quinnipiac University Swing State poll found that by margins of 8 to 14 percentage points voters in Florida, Ohio and Pennsylvania are skeptical of Clinton's trustworthiness.

In Florida, 51% of voters hold the negative view of Clinton, compared to 43% who feel she is trustworthy. In Ohio, 53% of voters find Clinton not trustworthy, compared to 40% who do. And in Pennsylvania, 54% of voters don't find her honest, while 40% do.

"I think it's understandable that when questions are raised, people maybe are thinking about them and wondering about them," Clinton said.

"But I have every confidence that during the course of this campaign, people are going to know who will fight for them, who will be there when they need them, and that's the kind of person I am and that's what I will do, not only in a campaign but as president," she said.

Photos: Hillary Clinton's life in the spotlight Hillary Clinton accepts the Democratic Party's nomination for president at the Democratic National Convention in Philadelphia on July 28, 2016. The former first lady, U.S. senator and secretary of state was the first woman to lead the presidential ticket of a major political party. Hide Caption 1 of 43 Photos: Hillary Clinton's life in the spotlight Before marrying Bill Clinton, she was Hillary Rodham. Here she attends Wellesley College in Massachusetts. Her commencement speech at Wellesley's graduation ceremony in 1969 attracted national attention. After graduating, she attended Yale Law School. Hide Caption 2 of 43 Photos: Hillary Clinton's life in the spotlight Rodham was a lawyer on the House Judiciary Committee, whose work led to impeachment charges against President Richard Nixon in 1974. Hide Caption 3 of 43 Photos: Hillary Clinton's life in the spotlight In 1975, Rodham married Bill Clinton, whom she met at Yale Law School. He became the governor of Arkansas in 1978. In 1980, the couple had a daughter, Chelsea. Hide Caption 4 of 43 Photos: Hillary Clinton's life in the spotlight Arkansas' first lady, now using the name Hillary Rodham Clinton, wears her inaugural ball gown in 1985. Hide Caption 5 of 43 Photos: Hillary Clinton's life in the spotlight The Clintons celebrate Bill's inauguration in Little Rock, Arkansas, in 1991. He was governor from 1983 to 1992, when he was elected President. Hide Caption 6 of 43 Photos: Hillary Clinton's life in the spotlight Bill Clinton comforts his wife on the set of "60 Minutes" after a stage light broke loose from the ceiling and knocked her down in January 1992. Hide Caption 7 of 43 Photos: Hillary Clinton's life in the spotlight In June 1992, Clinton uses a sewing machine designed to eliminate back and wrist strain. She had just given a speech at a convention of the International Ladies' Garment Workers Union. Hide Caption 8 of 43 Photos: Hillary Clinton's life in the spotlight During the 1992 presidential campaign, Clinton jokes with her husband's running mate, Al Gore, and Gore's wife, Tipper, aboard a campaign bus. Hide Caption 9 of 43 Photos: Hillary Clinton's life in the spotlight Clinton accompanies her husband as he takes the oath of office in January 1993. Hide Caption 10 of 43 Photos: Hillary Clinton's life in the spotlight The Clintons share a laugh on Capitol Hill in 1993. Hide Caption 11 of 43 Photos: Hillary Clinton's life in the spotlight Clinton unveils the renovated Blue Room of the White House in 1995. Hide Caption 12 of 43 Photos: Hillary Clinton's life in the spotlight Clinton waves to the media in January 1996 as she arrives for an appearance before a grand jury in Washington. The first lady was subpoenaed to testify as a witness in the investigation of the Whitewater land deal in Arkansas. The Clintons' business investment was investigated, but ultimately they were cleared of any wrongdoing. Hide Caption 13 of 43 Photos: Hillary Clinton's life in the spotlight The Clintons hug as Bill is sworn in for a second term as President. Hide Caption 14 of 43 Photos: Hillary Clinton's life in the spotlight The first lady holds up a Grammy Award, which she won for her audiobook "It Takes a Village" in 1997. Hide Caption 15 of 43 Photos: Hillary Clinton's life in the spotlight The Clintons dance on a beach in the U.S. Virgin Islands in January 1998. Later that month, Bill Clinton was accused of having a sexual relationship with former White House intern Monica Lewinsky. Hide Caption 16 of 43 Photos: Hillary Clinton's life in the spotlight Clinton looks on as her husband discusses the Monica Lewinsky scandal in the Roosevelt Room of the White House on January 26, 1998. Clinton declared, "I did not have sexual relations with that woman." In August of that year, Clinton testified before a grand jury and admitted to having "inappropriate intimate contact" with Lewinsky, but he said it did not constitute sexual relations because they had not had intercourse. He was impeached in December on charges of perjury and obstruction of justice. Hide Caption 17 of 43 Photos: Hillary Clinton's life in the spotlight The first family walks with their dog, Buddy, as they leave the White House for a vacation in August 1998. Hide Caption 18 of 43 Photos: Hillary Clinton's life in the spotlight President Clinton makes a statement at the White House in December 1998, thanking members of Congress who voted against his impeachment. The Senate trial ended with an acquittal in February 1999. Hide Caption 19 of 43 Photos: Hillary Clinton's life in the spotlight Clinton announces in February 2000 that she will seek the U.S. Senate seat in New York. She was elected later that year. Hide Caption 20 of 43 Photos: Hillary Clinton's life in the spotlight Clinton makes her first appearance on the Senate Environment and Natural Resources Committee. Hide Caption 21 of 43 Photos: Hillary Clinton's life in the spotlight Sen. Clinton comforts Maren Sarkarat, a woman who lost her husband in the September 11 terrorist attacks, during a ground-zero memorial in October 2001. Hide Caption 22 of 43 Photos: Hillary Clinton's life in the spotlight Clinton holds up her book "Living History" before a signing in Auburn Hills, Michigan, in 2003. Hide Caption 23 of 43 Photos: Hillary Clinton's life in the spotlight Clinton and another presidential hopeful, U.S. Sen. Barack Obama, applaud at the start of a Democratic debate in 2007. Hide Caption 24 of 43 Photos: Hillary Clinton's life in the spotlight Obama and Clinton talk on the plane on their way to a rally in Unity, New Hampshire, in June 2008. She had recently ended her presidential campaign and endorsed Obama. Hide Caption 25 of 43 Photos: Hillary Clinton's life in the spotlight Obama is flanked by Clinton and Vice President-elect Joe Biden at a news conference in Chicago in December 2008. He had designated Clinton to be his secretary of state. Hide Caption 26 of 43 Photos: Hillary Clinton's life in the spotlight Clinton, as secretary of state, greets Russian Prime Minister Vladimir Putin during a meeting just outside Moscow in March 2010. Hide Caption 27 of 43 Photos: Hillary Clinton's life in the spotlight The Clintons pose on the day of Chelsea's wedding to Marc Mezvinsky in July 2010. Hide Caption 28 of 43 Photos: Hillary Clinton's life in the spotlight In this photo provided by the White House, Obama, Clinton, Biden and other members of the national security team receive an update on the mission against Osama bin Laden in May 2011. Hide Caption 29 of 43 Photos: Hillary Clinton's life in the spotlight Clinton checks her Blackberry inside a military plane after leaving Malta in October 2011. In 2015, The New York Times reported that Clinton exclusively used a personal email account during her time as secretary of state. The account, fed through its own server, raises security and preservation concerns. Clinton later said she used a private domain out of "convenience," but admits in retrospect "it would have been better" to use multiple emails. Hide Caption 30 of 43 Photos: Hillary Clinton's life in the spotlight Clinton arrives for a group photo before a forum with the Gulf Cooperation Council in March 2012. The forum was held in Riyadh, Saudi Arabia. Hide Caption 31 of 43 Photos: Hillary Clinton's life in the spotlight Obama and Clinton bow during the transfer-of-remains ceremony marking the return of four Americans, including U.S. Ambassador Christopher Stevens, who were killed in Benghazi, Libya, in September 2012. Hide Caption 32 of 43 Photos: Hillary Clinton's life in the spotlight Clinton ducks after a woman threw a shoe at her while she was delivering remarks at a recycling trade conference in Las Vegas in 2014. Hide Caption 33 of 43 Photos: Hillary Clinton's life in the spotlight Clinton, now running for President again, performs with Jimmy Fallon during a "Tonight Show" skit in September 2015. Hide Caption 34 of 43 Photos: Hillary Clinton's life in the spotlight Clinton testifies about the Benghazi attack during a House committee meeting in October 2015. "I would imagine I have thought more about what happened than all of you put together," she said during the 11-hour hearing. "I have lost more sleep than all of you put together. I have been wracking my brain about what more could have been done or should have been done." Months earlier, Clinton had acknowledged a "systemic breakdown" as cited by an Accountability Review Board, and she said that her department was taking additional steps to increase security at U.S. diplomatic facilities. Hide Caption 35 of 43 Photos: Hillary Clinton's life in the spotlight U.S. Sen. Bernie Sanders shares a lighthearted moment with Clinton during a Democratic presidential debate in October 2015. It came after Sanders gave his take on the Clinton email scandal. "The American people are sick and tired of hearing about the damn emails," Sanders said. "Enough of the emails. Let's talk about the real issues facing the United States of America." Hide Caption 36 of 43 Photos: Hillary Clinton's life in the spotlight Clinton is reflected in a teleprompter during a campaign rally in Alexandria, Virginia, in October 2015. Hide Caption 37 of 43 Photos: Hillary Clinton's life in the spotlight Clinton walks on her stage with her family after winning the New York primary in April. Hide Caption 38 of 43 Photos: Hillary Clinton's life in the spotlight After Clinton became the Democratic Party's presumptive nominee, this photo was posted to her official Twitter account. "To every little girl who dreams big: Yes, you can be anything you want -- even president," Clinton said. "Tonight is for you." Hide Caption 39 of 43 Photos: Hillary Clinton's life in the spotlight Obama hugs Clinton after he gave a speech at the Democratic National Convention in Philadelphia. The president said Clinton was ready to be commander in chief. "For four years, I had a front-row seat to her intelligence, her judgment and her discipline," he said, referring to her stint as his secretary of state. Hide Caption 40 of 43 Photos: Hillary Clinton's life in the spotlight Clinton arrives at a 9/11 commemoration ceremony in New York on September 11. Clinton, who was diagnosed with pneumonia two days before, left early after feeling ill. A video appeared to show her stumble as Secret Service agents helped her into a van. Hide Caption 41 of 43 Photos: Hillary Clinton's life in the spotlight Clinton addresses a campaign rally in Cleveland on November 6, two days before Election Day. She went on to lose Ohio -- and the election -- to her Republican opponent, Donald Trump. Hide Caption 42 of 43 Photos: Hillary Clinton's life in the spotlight After conceding the presidency to Trump in a phone call earlier, Clinton addresses supporters and campaign workers in New York on Wednesday, November 9. Her defeat marked a stunning end to a campaign that appeared poised to make her the first woman elected US president. Hide Caption 43 of 43

Asked whether she played a role in the sentiment reflected in polls that she's not trustworthy, Clinton said: "This has been a theme that has been used against me and my husband for many, many years. And at the end of the day, I think voters sort it all out."

She similarly dismissed questions about her use of a personal email address on a private server while serving as secretary of state.

Clinton said she turned over all the emails -- including some which show her using a secured fax machine, or asking for iced tea during meetings -- that had anything to do with public business, and that she broke no laws in sticking with one device because she's not technically savvy.

"This is being blown up with no basis in law or in fact. That's fine, I get it -- this is being, in effect, used by the Republicans in the Congress. OK," Clinton said. "But I want people to understand what the truth is, and the truth is, everything I did was permitted and I went above and beyond what was expected."

If elected president, Clinton said she doesn't have any plans to push for the closure of the Clinton Foundation -- which has faced criticism for accepting foreign contributions during her tenure as America's top diplomat.

"I have no plans to say or do anything about the Clinton foundation other than to say I am proud of it and I think for the good of the world, its work should continue," she said.

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The interview spanned a broad range of topics -- among them a discussion of adding a woman to the $10 bill. Clinton declined to select a favorite woman for the honor, but suggested a woman should instead go on a $20.

"I don't like the idea that as a compromise you would basically have two people on the same bill. One would be a woman. That sounds pretty second class to me," Clinton said. "So I think a woman should have her own bill."

Nor would she pick which Saturday Night Live actress, Amy Poehler or Kate McKinnon, plays the best Hillary Clinton.

"Amy's a friend of mine and Kate's doing a great job. You're not going to get me to pick one or the other," she said. "I think I'm the best Hillary Clinton."