Garrett responded Tuesday by saying every player and coach is fighting for their jobs.
"Ever since I've been in this league, as a player and as a coach, I think everybody, each and every day, is playing and coaching for their jobs," Garrett said after Tuesday’s organized team activity. "That's the nature of this thing and that's what makes the NFL great. You come here to work every day.
“Every day is important as a coach, as a player, and we're trying to get ourselves better each and every day so we can become the team we want to be."
The Cowboys haven't reached the postseason under Garrett, who is entering the third season of a four-year deal as head coach.
It has been a difficult offseason for Garrett. He allowed his brother, John, to leave the franchise and become the tight ends coach at Tampa Bay. Defensive coordinator Rob Ryan was let go by Jones, despite the strong relationship he had with Garrett. And Garrett could end up relinquishing the play-calling duties for 2013. Jones has said it's up to Garrett to make a final decision regarding the playcaller.
The offseason also included Jones saying quarterback Tony Romo will have more say in the offense. Jones, however, is confidence in Garrett's abilities to push the Cowboys to the postseason.
"Well, no, no he's not ... to the last question: Is Jason coaching for his job? No," Jones told the NFL Network in an interview from the NFL's spring meetings in Boston that aired last week. "What we're doing is taking the assets that we have, and Jason being right at the top and certainly our premier asset, and we're using them to the best of our ability."