That follows last week's and, according to People magazine, a Christmas visit by Elizabeth with the toddler.
In addition, a soon-to-be-released book by a longtime former aide to John Edwards claims to offer details about the Edwards marriage, and John's romps.
A friend of Elizabeth says the couple has separated. Under North Carolina law, they must be separated for a year before they can divorce.
In a statement released to The Associated Press late Wednesday night, John says, "It is an extraordinarily sad moment, but I love my children more than anything and still care deeply about Elizabeth."
John and Elizabeth were law students when they met at the University of North Carolina. They married in 1977 and had four children.
But, notes CBS News National Correspondent Jeff Glor, their marriage was tested over time by life's tragedies. In 1996, their oldest child, Wade, was killed in a car accident. In 2004, Elizabeth Edwards revealed that she had been diagnosed with breast cancer. Four years later, the cancer returned and was no longer curable.
The couple weathered those storms.
Then, in December 2006, the first public crack in the marriage, when Elizabeth learned of her husband's infidelity. Still, they stayed together.
But slowly, the details of John's infidelity kept coming out, culminating last week, when he admitted he'd fathered a child with mistress, Rielle Hunter.
Now, in "The Politician," a tell-all book by the former John Edwards aide, Andrew Young, lurid details are given of what Young says are John's sexual exploits.
"I think," Politico.com's Andy Barr told CBS News, "this is like the final, devastating blow that's just a total embarrassment for John Edwards."
Glor observes that, "No one emerges from the book looking very good -- not John Edwards, not Rielle Hunter, not Elizabeth Edwards, who has been characterized recently as someone who was willing to look past some of her husband's issues because she wanted to be in the White House even more than John. A spokesperson for Elizabeth says the book contains many falsehoods and exaggerations and is 'hurtful.' "
Yet, it was meeting John's love-child that was the final straw for Elizabeth, according to People, which interviewed her sister and some friends of the couple to get its inside look.
The magazine's executive editor, Betsy Gleick, told "Early Show" co-anchor Harry Smith Thursday that, "As recently as Christmas, so just exactly a month ago, Elizabeth reached out to this little girl, the daughter of her husband's mistress, and brought this little girl Christmas presents, and was excited when the girl liked the Christmas presents, and insisted that the little girl, Francis Quinn, take a picture with Daddy. So, as recently as a month ago, Elizabeth was trying to embrace this new reality in her life.
"And, as we all know, she basically -- she couldn't do it. She's done."
Gleick says friends of both Elizabeth and John paint portrait of a couple "trying to keep it together under really difficult and unusual circumstances."
She points out that both have denied "a lot of the things in that book. But, clearly, what was going on behind the scenes was much more complicated and much less perfect than what they tried to present to the public."
Gleick says "the most important message" from Elizabeth's sister, Nancy Anania, "is that Elizabeth really has now said,' I've had it, I am moving on with my life,' and she is trying to embrace the next chapter of her life."