Stormy Daniels' attorney argues 'cover-ups matter'

Daniels, whose legal name is Stephanie Clifford, filed suit against Trump on Tuesday, alleging that he never signed a hush agreement regarding an alleged sexual encounter between the two and therefore the agreement is void.

White House press secretary Sarah Sanders said Wednesday that "arbitration was won in the President's favor" regarding the case. The statement is an admission that the nondisclosure agreement exists and that it directly involves Trump. It was the first time the White House had admitted the President was involved in any way with Clifford.

Trump's personal lawyer, Michael Cohen, said last month that he paid $130,000 of his own money to Clifford right before the 2016 election in exchange for her silence about the matter. But both Cohen and the White House have denied any sexual encounter between the President and Clifford.

"The cover-up is that you have attorney (Michael) Cohen claiming that Donald Trump never knew anything about this. You have the White House claiming Donald Trump never knew anything about this. That is going to be shown to be patently false," Michael Avenatti, the attorney for Daniels, said in an interview Friday on CNN's "New Day."

Avenatti said he has further "substantial evidence and facts that were not included in the complaint" to back up his claims, though he said he was "not going to lay all of our cards out on the table" Friday.

"When that evidence and those facts come to light, the American people are going to conclude that attorney Cohen and the White House have not shot straight with them on this," he alleged.

Avenatti said that Daniels would "absolutely" pay back the $130,000 payment if she's "ultimately ordered to do that to speak openly and honestly" or if Trump and Cohen want to "admit that (Trump) know about the deal and didn't sign it."