Smith, hired on a 10-month contract to replace the ousted Bobby Petrino, was asked if he would like to have the job moving forward.
The questioner noted that speculation it would take a 14-0 mark and national championship for the 63-year-old to do that.
"Well, certainly," Smith said. "Do I look stupid. Wait, don't answer that."
Smith, quarterback Tyler Wilson, tailback Knile Davis and linebacker Tenarius Wright represented the Razorbacks on a day when six teams were highlighted.
"I'm definitely blessed to have the opportunity and was definitely blessed to be back at the University of Arkansas," Smith said. "In coming back to the university, I know we had a real good football team that possibly has the capabilities of being a great football team with a great senior class to lead us."
"As I came back after spring ball, the energy in the room, the energy around our players has been exceptional," Smith said. "Our senior class…I think they took a little adversity they had, they locked up, came together and said we are going to be better because of it and that's what they've done."
Smith said that Arkansas players – who gave him a standing ovation in a meeting before his official press conference – have welcomed him with open arms.
"My coming in, my walking through the door, it was unbelievable the reception that I got," Smith said. "I had to wipe the tears away because of kids and the reception that I got.
"…I told them that this is one thing we are going to continue to reiterate – this is a program, this is not about somebody leaving, somebody coming, this is one program, okay?" Smith added. "We're all a part of it as players, as coaches, as fans, as the student body, we all have to relish our position as being part of this program."
Smith made it clear that the team's goal is to win the national championship game.
"We have one goal and we are not bashful about reiterating that goal," Smith said. "That goal is to win in Miami. Our goal is to be a national championship and that's what we want to get done."
The Razorback players - some of whom got calls from a humbled Petrino last week - made it clear that they are offended because of people doubting them with the loss of their former coach.
"I have a chip on my shoulder," Wilson said. "We all have a chip on our shoulders."
Davis said those expected Arkansas to fail are entitled to their opinion, but are wrong.
"That is their opinion and I can't do anything about that," Davis said. "We'll see at the end of the season…We are going to win and win big."
Wright echoed that sentiment while saying there may be a new face at the top of the program, but the goals remain the same.
"My opinion on that is that we have a new face leading us out of the tunnel and with the seniors we have coming back, we all know what it takes," Wright said. "We all sit in the same meeting room with Bobby Petrino when he broke down what it takes to be a champion. We still have those goals and believe in what he has taught us.
"It is only going to help us mold this team together because we think it is our job to keep people in line as seniors," Wright said.
Wilson said this could very well end up being the best Arkansas team he has been on in his five years with the program.
"You guys can say what you want, but I witnessed the best spring that I have had since I have been here," Wilson said. "With that, I think we could have a better season. "I was here during the five-win season my freshman year, here during the seven-win season my redshirt season, the 10-win season and the 11-win season if you do the math," Wilson said. "We are in good shape going into this season."
He also noted that Smith was a different coach, but not the goofball some might get from his fun-loving personality.
"The difference (from Petrino) is that Coach Smith walks in and has an ability to single a guy out or discipline someone – and then wink at them after he says it," Wilson said. "He lets you know that you are still my guy, I am still on your side, but I want you to do the right thing. That is something a little bit different, something minor that might be a little unique.
"We have some staff members, some coordinators that can get on you and are disciplinarians, but we also have a head coach that can discipline in the manner that he needs to do so," Wilson added.
Davis said the public Smith is not like the one he presents to his team when it is time to get serious.
"For y'all, he is a comedy act, but not behind the scenes where there is not a lot of comedy going on," Davis said. "I think John L. just brings a different style of coaching. He is different from Bobby, but I think it is good for us. He has been here before, we still have the same coaching staff that we have had. I think we are good to go."
John L. Smith speaks at the SEC Media Days on Tuesday.