The Monday night address to the nation, in which Mr. Clinton admitted that he had an inappropriate relationship with former White House intern Monica Lewinsky, included an expression of contrition to his wife.
"I misled people, including even my wife. I deeply regret that," Mr. Clinton told the nation.
CBS News Correspondent Eric Engberg reports that it is Mrs. Clinton's staunch support that has given the president such a boost in recent months in the opinion polls.
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The Rev. Jesse Jackson, a civil-rights leader and former presidential candidate, was called this weekend to counsel the first family. Jackson later described Mrs. Clinton as still being strongly committed to her marriage, but humiliated.
"The marriage vow is for better and for worse," Jackson said on CBS This Morning. "For too many people, when worse comes, it's divorce time. For her, when worse comes, it's faith time."
Jackson said Mrs. Clinton's maturity "obligates her through her humiliation and Bill's sense of embarrassment, to be able to keep that family together, not to isolate Chelsea but to insulate her."
Carl Anthony, a friend of Mr. Clinton and a historian of first ladies, also mentioned Mrs. Clinton's faith, which he said "has always been a foundation for her."
Anthony says Mrs. Clinton will deal with this "as many spouses across the country and through the generations have had to deal with this, by fits and starts and on her own time."
Don Baer, a former White House speechwriter who is a friend of the first family, pointed out that, whether or not Mrs. Clinton believes the president about Lewinsky, he is sure she believes in him.
"That's a very important thing," Baer said on This Morning. "She thinks of him as the most gifted politician of our generation. She believes that quite fervently. She believes he was destined to be president, and he was destined to be a great president.
"I think it's important to remember that she does love the president, she loves her daughter, but she also believes very much in his political agenda and missin."
Baer said he felt particularly sympathetic toward Mrs. Clinton because he remembers being struck, when as a reporter he first interviewed her in 1991, by how "human and sensitive" she was.
Both Anthony and Margaret Carlson, a writer for Time magazine, say divorce is not an option.
"She's invested her life in this career, as did Eleanor Roosevelt, even as did Jacqueline Kennedy in the 10 years of her marriage," said Anthony. "You don't just walk away from that kind of an investment."
A Yale-educated lawyer who was a partner in a Little Rock law firm until her husband was elected president, Mrs. Clinton has a mission as a first lady and a commitment to projects on a global scale, and she wants to see them through to completion, Anthony said.
"If she was married to a used car salesman, would she
still be there? She wouldn't," said Carlson. "But she's married to a president, and she is the first lady. So they both are doing this.
"They are so entangled that they can't get apart."
Carlson said she was particularly sympathetic to Chelsea.
"No child disbelieves. A wife might have doubt; a child believes totally," she said. "You can just imagine the excruciating pain to have told Chelsea about this. And the cheater never thinks the child is going to find out. Yet sometimes they do, and I think this is a moment that will take years of repair."
Spokeswoman Marsha Berry says the first lady is focused on the speech she'll deliver in Northern Ireland next month. She is just starting a two-week family vacation in one of her favorite resorts.
A senior aide says Mrs. Clinton has no plans to make any public comments in the next few days. The conventional wisdom at the White House is that she can show her support for her husband by appearing with him publicly during their vacation.
Nearly everyone agrees that the next two weeks, when the family is vacationing on Martha's Vineyard, will be critical for the family.
"They will try to have some private time," said Baer. "They are going on vacation. I think this is a period for healing within this family as well as for the country."
Carlson said the first couple might be better off staying in Washington and sticking to their usual busy schedules.
"Family vacations can be tough on people - even when they are getting along well - in the sense that you're out of your normal schedule, and you're confronted with each other eight hours a day, 12 hours a day, for the first time in a long time."
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