I once watched an apology rebuffed. A young child said something hurtful to a grown-up dinner guest. After prompting from her mother, the child apologized. “I’m sorry,” the 6-year-old said in a dutiful and not completely sincere tone. “Sorry,” replied the grown-up, “is not enough.”

I think of this frequently when I watch the renewed and refurbished Newt Gingrich, who is at the top of the 2012 Republican heap, spin his tale of sin and redemption — in hopes that primary voters will find him sorry enough.

Here is how he explains his serial marital infidelities. In the 1990s, Gingrich was working so hard in Congress that he felt “truly hollow.”

“I found myself as an emerging national figure trying to understand where I had failed and why I was empty,” he told an audience in Iowa before Thanksgiving. And so he turned to God. “I feel that had I not had that experience . . . I might literally have collapsed totally.” (The timeline here is obscure: Did Gingrich turn to God before or after he cheated on his second wife with the woman who would become his third?)

The job before him, of turning his life around — which Gingrich parenthetically says “required a great deal of pain, some of which I have caused others, which I regret deeply” — forced the candidate “to go to God to seek both reconciliation but also to seek God’s acceptance.” Gingrich in effect, said “I’m sorry” to God.

It’s easy to be cynical when a politician, at a high-stakes moment, stands before his public and claims to have apologized to God. How can voters tell whether the candidate wants, like a 6-year-old, to be forgiven so he can get dessert (or his party’s nomination) or whether he’s truly sorry?

The answer seems to lie in the petitioner’s display of authenticity. That is, do people believe in his remorse? “I ask you,” said President Bill Clinton in the midst of the Lewinsky scandal in 1998, “to share my prayer that God will search me and know my heart.” Politically, this apology succeeded. It helped Clinton keep his job, though his reputation as a cad was by then cemented.

George W. Bush, on the other hand, made his confession to God a centerpiece of his 2000 presidential campaign. People believed — and liked — his once-was-drunk-but-now-am-sober-narrative.

Theologically, though, asking forgiveness is more than just posturing. In the Catholic tradition, it requires confession, reparation and penance, and Gingrich, a recent convert to Catholicism, does not come across as a down-on-his-knees kind of guy.

The first question some religious conservatives have about Gingrich’s admission of sin is this: Has he made reparations to the cheated-upon wives? “If you’ve wronged somebody else, the Scriptures teach that you have to go to that person and ask for forgiveness,” says Cal Thomas, a syndicated columnist who once ran PR for the Rev. Jerry Falwell. “I would ask from a theological-biblical standpoint, ‘Did you go to the persons you wronged and ask for their forgiveness?’ Whether they grant it or not isn’t as important as you seeking it.”

Penance requires humility. In the earliest days of the Catholic Church, adulterers were instructed to do their penance publicly, by wearing hair shirts, for example, or standing in stress positions — arms outstretched like a crucifix — for hours at a time.

But Gingrich is no monk. He loves food and wine and was discovered this year to have carried as much as $500,000 in debt at Tiffany & Co. in 2005 and 2006. More serious, from a theological perspective, is the absence of humility Gingrich displays in his political rhetoric.

In his 1998 speech, Clinton spoke of needing God’s help “to give the very forgiveness I seek,” but Gingrich shows no signs of understanding the profound nature of this kind of petition. Instead, he inflames and divides, accusing the U.S. government of acting as a “secular socialist machine” (from the title of his book) and “oppress[ing] the American people against their own values.”

I asked the Republican political consultant and Catholic Mary Matalin whether she thought Gingrich’s plea for forgiveness would absolve him of bad past behavior in the eyes of the public.

She answered thus, in an e-mail: “For Catholics, who are humbled by and grateful for God’s Grace in all things, forgiveness is a first among equals. We are all fallen, yet He loves each of us. . . . We pray, God answers; only He can determine the motivation of the prayers.”

In other words, only God knows if Newt’s sorry enough.