In full damage control, Michelle and Jim Bob Duggar set out Wednesday not only to restore the image of a sprawling TV family dynasty, but also to preserve a sprawling TLC hit. Indeed, the TLC hit "19 Kids and Counting," is unofficially in limbo following reports that eldest son, Josh, 27, had molested underage girls when he was 14.

Alternately anguished and defiant, both Duggar parents insisted during an interview with Fox News' Megyn Kelly on "The Kelly File" that the children who were molested -- confirming widespread media reports that they included four daughters -- had been asleep during the physical contact initiated by their son.

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Jim Bob Duggar told Kelly that upon finding out from their son what he had done, "we went through the most darkest times our family has ever gone through." Michelle Duggar said, "We were shocked, devastated. No parent is prepared for a trauma like that," while adding, "There was so much grief in our hearts. I think as parents we felt we're failures, you know? Here we tried to raise our kids to -- to do what's right and know what's right. And yet, one of our children made really bad choices and I think as a parent we were just -- we were devastated."

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They said they later sent Josh to a Christian counseling service and in 2005 went with him to speak to an Arkansas state trooper, Joseph T. Hutchens -- who is currently serving a 56-year sentence over child pornography charges.

Kelly also challenged them over critics' charges that they were hypocritical about their various positions, notably on LGBT rights, given their family's past. "I know everyone of us has done something wrong," said Michelle. "This is about an agenda and about people who are purposely trying to bring things out to hurt and to slander us."

Asked by Kelly whether they believe the TLC program will be canceled, Jim Bob Duggar said, "at this point, our family is trying to regroup from these attacks."

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Fox News will air a one-hour special Friday night in which Kelly interviews Jill and Jessa Duggar, who identified themselves on Wednesday as victims of their brother.