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Mr. Gingrich vowed to stay positive, even as he said Mr. Romney had “no willingness to stand up and tell the truth.”

Mr. Paul is campaigning this week in Iowa, a wide-open state he potentially could win. He drew large crowds at several town-hall meetings in eastern Iowa on Wednesday.

But few campaign veterans think Mr. Paul, whose strong libertarian views give him an intense but limited following, can draw enough support nationwide to win the nomination.

Mr. Gingrich hopes to do well enough in the first two contests to make it to South Carolina and Florida. They border Georgia, which he represented in Congress for 20 years, ending in 1999.