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He’s got little money and even less of a staff, but Lincoln Chafee is not giving up on his dream of becoming president.

The former senator and governor from Rhode Island is taking a slow and steady approach to challenging Hillary Rodham Clinton for the Democratic Party’s nomination. Weaving jabs at Mrs. Clinton’s credibility with liberal policy proposals, Mr. Chafee is holding out hope that his understated manner still has time to gain traction with voters.

“There’s still more to be done on the fund-raising and the apparatus and the organization,” Mr. Chafee said at a breakfast hosted by The Christian Science Monitor on Tuesday. “But that doesn’t discount what I do bring to the table.”

Formerly a Republican and independent, Mr. Chafee brings legislative and executive experience at the local and state level. He also brings a credible voice to criticize Mrs. Clinton’s support for the 2003 invasion of Iraq, which he opposed.

On Tuesday, Mr. Chafee acknowledged that he is facing unusual headwinds in going up against a challenger such as the former secretary of state.

“The reality is that Secretary Clinton has a huge head start, has all the endorsements and all the money, and the rest of us are scrambling,” Mr. Chafee said.

The challenge has been even harder because of the emergence of Senator Bernie Sanders as the leading alternative to Mrs. Clinton and the presence of former Gov. Martin O’Malley, who also leads Mr. Chafee in most polls.

Mr. Chafee said that he wants to use Jimmy Carter’s campaign as a model, “plodding away” and talking about the issues that matter most to him and, hopefully, eventually catching on.

Not shying away from needling Mrs. Clinton, Mr. Chafee said that she has a lot of “self-inflicted wounds,” pointing to questions about her use of a private email account as secretary of state and foreign donations to the Clinton Foundation. However, he said that he needed to be careful in his criticism of her because the election of a Democratic president remains his priority.

In the meantime, Mr. Chafee will continue making trips to Iowa and New Hampshire to court voters while keeping his operation as lean as possible.

“I’ve got to pace my budget,” said Mr. Chafee, whose net worth is more than $40 million. “I’m not going into debt, not going to to spend more than I raise.”

What Lincoln Chafee Would Need to Do to Win Lincoln Chafee, a former Rhode Island governor and senator, has entered the race for the Democratic nomination for president. Here is what he will need to do if he hopes to win.