Deal Hudson, president of Catholic Advocate, a conservative group, said that if Mrs. Gingrich “wants to be first lady,” she would probably have to discuss their relationship as well.

So far she has not. Both Gingriches declined to be interviewed for this article.

“They would say they wished they had met in a different time in their lives under different circumstances,” said Jackie Cottrell, a friend who worked with Mrs. Gingrich as a staff member on Capitol Hill. “But it’s important to note that they brought their family together in a loving way.”

Mr. Gingrich took up golf because his wife plays; she has adopted his political agenda. In 2009, after years of attending Mass to hear her sing in her church choir, he converted to Catholicism. And when Mrs. Gingrich, who plays French horn with the city band in Fairfax, Va., appears in concerts, her husband totes her black instrument case. “I’m a band groupie and a choir groupie,” Mr. Gingrich likes to say.

How eager she is for him to run after he has been out of office since 1999 is a matter of discussion among their friends. Vin Weber, the former Republican congressman from Minnesota, said he is “quite convinced” Mrs. Gingrich is happily on board. “They’ve been out of public life,” Mr. Weber said, “and I think she misses the excitement of that.”

Others say she wants her husband to run because he wants to. She has hired Ms. Olson as her chief of staff; she is also writing a children’s book, due out in September — just in time for her to go on a book tour and reintroduce herself to the public as the primary race heats up.

“I think she has stepped out of her comfort zone more to promote the movies and the books and has found that she enjoyed that,” said Ms. Cottrell. “That’s been a little bit of a toe in the water.“