As always, Mr. Gingrich continues to mix the abstract and the more politically concrete.

The man who introduced the Contract with America in 1994, which still stands as a gold standard of political branding, now has a snappier jingle for today’s shorter attention span. The message is so concise that he pulls it from the breast pocket of his suit, no matter if he is delivering an intimate dinner speech or addressing a large audience, as he did recently at the Conservative Political Action Conference.

The note card reads: “2 + 2 = 4.”

It is an elementary lesson on spending and debt, he said, that has eluded the Obama administration. He uses it to present his broader view that the next presidential election should be a major debate over the size and scope of government.

When President Obama changed his position last week and said he believed that the 1996 law barring federal recognition of same-sex marriages was unconstitutional, Mr. Gingrich waited a full day to offer his reaction. In a statement on Thursday, Mr. Gingrich kept his criticism confined to process, rather than the merits of marriage, saying: “The president is replacing the rule of law with the rule of Obama.”

It remains an open question how a new inspection of Mr. Gingrich’s record would hold up to scrutiny by voters, including his own spending votes and the 1995 government shutdown, but his advisers believe that it could be well received, given the sentiment of Tea Party supporters. And in the early going, Mr. Gingrich appears to be getting another look from religious conservatives, especially Catholics, a traditional swing constituency.

Before and after his appearance here, dozens of people lined up to buy books, movies and other mementos that help finance the operations of Mr. Gingrich’s array of business enterprises and provide a window into his growing popularity among some social conservatives. Mr. and Mrs. Gingrich sat for more than an hour signing inscriptions, with his best-selling book, “Rediscovering God in America,” a particularly popular item on this snowy night in Ohio.

Dr. Jack Willke, an early leader in the anti-abortion movement in Ohio and across the country, was among those waiting for an autograph. Dr. Willke said he was delighted that Mr. Gingrich had increased the role of faith in his public appearances, something that he said he did not recall during Mr. Gingrich’s tenure as speaker of the House.

“We were there long before he was,” Mr. Willke said. “It was never a big public thing for Newt, but he’s surfaced now as considerably more so.”