Gingrich pursued an approach Perry used in the earlier debate.
"If there's anything that's in there that's going to help us lose the election, we should know before the election. If there's not, why not release it?" he said.
Gingrich released his own tax return during the day, reporting that he paid the IRS $613,517 in taxes on more than $3.1 million in income. He also donated about 2 percent of his income to charity.
His effective tax rate, roughly 31.6 percent of his adjusted income, was about double what Romney told reporters earlier this week he had paid.
Gingrich grappled with problems of a different, possibly even more crippling sort in a state where more than half the Republican electorate is evangelical.
In an interview scheduled to air on ABC News, Marianne Gingrich said her ex-husband had wanted an "open marriage" so he could have both a wife and a mistress. She said Gingrich conducted an affair with Callista Bistek — his current wife — "in my bedroom in our apartment in Washington" while she was elsewhere.
"He was asking to have an open marriage and I refused. That is not a marriage," she said in excerpts released by the network in advance of the program.
He said his two daughters from the first of his three marriages — the ex-wife making the accusations was the second of three — had sent a letter to ABC "complaining about this as tawdry and inappropriate."
In fact, the letter made no such accusations. Instead, Kathy Lubbers and Jackie Cushman wrote ABC that anyone who has endured a failed marriage "understands it is a personal tragedy filled with regrets, and sometimes differing memories of events."
Those weren't the only political events in the run-up to the Saturday primary. Television commercials for the remaining candidates and their allies ran virtually without letup, generally designed to diminish each other's support.
According to information made available to The Associated Press, targeted viewers in most regions of the state were watching an average of about six commercials a day paid for by Romney's campaign and Restore Our Future, a group supporting him. Gingrich, Paul, Santorum and their backers raised the total higher.
Santorum ran commercials likening Romney to Obama; Gingrich's cast the former speaker as the only candidate who could defeat the president this fall. In a sign of the shifting campaign, Restore Our Future stopped attacking Santorum so it could concentrate its fire on Gingrich.
Santorum, whose fortunes have ebbed since what appeared to be a narrow loss in Iowa, pronounced himself the winner there after all when state party officials in Des Moines announced he had finished 34 votes ahead of Romney instead of eight behind.
"There have been two contests. We won one," he said, and he proceeded to ridicule Romney and Gingrich as weak challengers to Obama. "How can you differentiate ourselves on the major issues of the day if we nominate tweedledum and tweedledee instead of someone who stood up and said, 'No'?" he said to one audience, referring to his opposition to a requirement to purchase health care coverage.
Iowa Republican chairman Matt Strawn said the party would not name an official winner because the results were so close and some votes couldn't be counted. Results from eight of the state's 1,774 precincts were not certified to the state party by Wednesday's 5 p.m. deadline.
It was Strawn who had stepped before a microphone shortly before 2 a.m. in Des Moines on Jan. 4 to declare Romney the victor.
That announcement propelled the former Massachusetts governor into New Hampshire, where he breezed to victory in the opening primary of the campaign a week later.
He arrived in South Carolina the following day, front-runner then for sure, now more shakily so.
Perry's withdrawal mimicked one earlier in the week by former Utah Gov. Jon Huntsman in that they both quit a few hours before a debate.
The similarities ended there, though. Huntsman endorsed Romney.