For instance, she has said in interviews and in testimony in a redistricting lawsuit involving her State Senate district that she was divorced by the time she was 19 and lived as a single mother in a trailer. Her campaign has since clarified that while she separated at 19 and lived in the trailer with her daughter, she filed for divorce at 20 and the divorce became final when she was 21.

Nor had she focused on the role of her second husband, Jeff Davis, whom she divorced after a nearly 17-year marriage. He told The Dallas Morning News that she left him the day after the final payment was made on the loan for Harvard. She has denied the claim. The Dallas newspaper also said he had won custody of their two children. Her campaign said the couple had joint custody.

In a letter released Tuesday, Ms. Davis’s daughters, who were 2 and 8 when Ms. Davis entered Harvard, issued full-throated defenses of her, saying that she was always a presence in their lives, even when away at law school, and that they had initially gone to Boston with her.

Amber Davis, 31, called the criticism of her mother “ludicrous.”

Dru Davis, 25, wrote: “I can tell you that my mom was a remarkable mother and continues to be so to this day. She was there on my first day of school and my last, and so many days in between. She never missed a school performance or a parent-teacher conference. Even if that meant she had to miss something else important.”

The issue has produced a freewheeling debate on social media and cable television that sometimes followed familiar partisan lines and sometimes crossed them.

A blog post by Ms. Palin, a daughter of the 2008 Republican vice-presidential nominee, Sarah Palin, whose teenage pregnancy became a social media moment of its own during the Republican convention, criticized Ms. Davis’s parenting history and compared Ms. Davis unfavorably to her mother.