Biden remains at the front of the pack because no one criticized him on Wednesday, Elleithee claimed Thursday on "Special Report."
"One of the biggest winners last night, honestly, was Joe Biden because no one touched him," he said.
"And while Warren had some good moments, Booker had good moments, Castro had a really good night, they helped themselves a bit, they didn't really change the overall contours of the race.
"Biden is still the front-runner and no one challenged him last night."
The former DNC communications director added it will be interesting to see how Biden is treated by fellow candidates when he is present on the stage Thursday evening in Miami.
Elleithee said that one candidate who had a regrettable moment after his debate appearance was New York City Mayor Bill de Blasio.
"The best thing Bill de Blasio has going for him is that there's another debate in a couple of hours that's going to take all the headlines away," he said.
De Blasio was criticized for quoting Cuban revolutionary Che Guevara when he spoke at the Miami airport in support of striking union workers on Thursday.
"Hasta la victoria siempre," the mayor said while holding a microphone.
He later apologized, tweeting he did not mean the comment in an offensive manner.
"I did not mean to offend anyone who heard it that way. I certainly apologize for not understanding that history," he said.
"I only meant it as a literal message to the striking airport workers that I believed they would be victorious in their strike."