Hillary Clinton met students taking part in a job skills program called YouthBuild in Las Vegas on the day before the Nevada caucuses. (Melina Mara/The Washington Post)

Democratic presidential candidate Hillary Clinton acknowledged in an interview that aired Sunday on CNN's "State of the Union" that she needs to prove she is driven not by selfish ambition but by a desire to improve voters' lives.

"I understand that voters have questions," the former secretary of state said in an interview that was taped late Saturday, after her victory in the Nevada caucuses. "I'm going to do my very best to answer those questions. I think there's an underlying question that maybe is really in the back of people's minds, and that is, you know, is she in it for us or is she in it for herself? I think that's a question that people are trying to sort through, and I'm going to demonstrate that I've always been the same person fighting for the same values, fighting to make a real difference in people's lives — long before I was ever in elected office, even before my husband was in the presidency. I know that I have to make my case."

Clinton was responding to a question from CNN anchor Jake Tapper about "trust" issues. A recent CBS News poll reinforced what previous surveys have found — that Clinton lags far behind rival Bernie Sanders when voters are asked whether the candidates are "honest and trustworthy." The CBS poll showed a 17-point advantage nationally for the Vermont senator.

Throughout the race, Clinton has refused to concede any connection between her trust deficit and her use of a private email server as secretary of state; she has said repeatedly that voters don't care about the issue, even as the FBI conducts an investigation into the security of her practice.

Clinton made no such admission in the CNN interview, either. But in acknowledging that some voters question her motive in seeking the nation's highest office, she at least conceded that trust is a real hurdle she needs to clear.