But Walker, who has expressed support for a national abortion ban without exceptions, vehemently denied the story, calling the abortion allegation a "flat-out lie," threatening a lawsuit against the outlet he has yet to file and saying he had no idea who the woman might be.Walker has been accused of repeatedly threatening his ex-wife's life, exaggerating claims of financial success and overstating his role in a for-profit program that is alleged to have preyed upon veterans and service members while defrauding the government.Earlier this year, after a story by The Daily Beast, Walker acknowledged the existence of three children he had not previously talked about publicly.During the Republican Senate primary, Walker openly backed a national ban on abortions with no exceptions for cases involving rape, incest or a woman's health being at risk - particularly notable at a time when the 1973 Roe v. Wade Supreme Court precedent had been overturned and Democrats in Congress had been discussing codifying abortion rights into federal law.When asked about his son's Tweets, Herschel Walker's campaign responded with a text pointing to a Tweet from Herschel Walker that says, "I LOVE my son no matter what.""