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Mr. Paul, the blunt-spoken Texas congressman, was campaigning Wednesday in Iowa, along with other candidates in the field. The race there remains unpredictable, as voters weigh electability against conservative credentials.

Jenny Turner, a 31-year-old wedding videographer from Mount Pleasant, Iowa, summed it up this way: “My heart is with Newt, but MittRomney is in the back of my mind.”

The bickering over negative ads has highlighted the role of so-called super-PACs, independent groups that may accept unlimited donations but are not supposed to directly coordinate with candidates. Such groups have sprung up to work on behalf of every serious Republican candidate after a U.S. Supreme Court decision last year that allowed individuals, unions and corporations to donate unlimited sums of money to outfits advocating the election or defeat of candidates.

On Tuesday, Mr. Gingrich and Mr. Romney decried the system, with Mr. Romney calling it a “disaster” and Mr. Gingrich branding it as a “nightmare,” but both benefit from super-PACs.

Two pro-Gingrich groups have started raising money, and Mr. Gingrich’s longtime aide Rick Tyler just signed on with one of them.

Mr. Romney‘s supporters, however, have had a yearlong head start in raising money. Restore Our Future is slated to spend roughly $3 million on ads, most of which paint Mr. Gingrich as an ethically-challenged Washington power broker.

Mr. Gingrich, who trails Mr. Romney badly in fundraising after a campaign implosion this year, said he would disavow any group that runs negative ads on his behalf.

In a sign of his fundraising and organizational deficiencies, Mr. Gingrich was rushing later Wednesday to Virginia, the state the former Georgia congressman now calls home, to help ensure he has the needed signatures to get on the ballot there.