Ty Cobb's comments came as House Democrats ramped up their investigations into the president, including two new wide-ranging inquiries launched on Monday.
The Yale-educated lawyer has served two former presidents and one vice president. He will now replace Ty Cobb, the White House has announced.
"The law firm of Larry, Mo and Curly, and of counsel Rudy, can't actually find out what the truth is," Scarborough said of Trump's legal team.
Trump hasn't committed to speaking with Mueller.
Cobb also echoed the call by Jay Sekulow and others for a second special counsel.
Trump's longtime backer says it's only a matter of time before the Russia probe and allegations of sexual misconduct take down the president.