Barber suffered a thigh injury against the New York Giants on Sept. 20, and he's still not fully recovered heading into Sunday's game against the Atlanta Falcons.
"I can tell you Barber is going to be in better shape than he was last week or two weeks ago," Jones said. "But Tashard is certainly earned and going to get a big part of the load."
Choice's carries have fluctuated since Barber's injury. He carried 14 times for 33 yards in a loss at Denver on Oct. 4, but had just eight carries in the overtime victory over Kansas City on Oct. 11. His 92-yard effort against the Chiefs included a 36-yard touchdown run.
Choice started three games last season while Barber was injured and rushed for 234 yards and one touchdown on 53 attempts.
Choice was supposed to be the Cowboys' third-down back this season, but he's moved up the depth chart after injuries to Barber and Felix Jones (knee).
Jones participated in practice Monday and moved around pretty good. His status for Sunday's game against Atlanta hasn't been determined, though he expects to play.
"We were pleased with how Felix moved around [Monday]," Jerry Jones said. "But we don't know how sore he's going to be [Tuesday]. I think what we've got, the strength of our team is the running back position. It's the most strength that we've had at any spot and we need to use it and we will use it."
Calvin Watkins covers the Cowboys for ESPNDallas.com. E-mail him at firstname.lastname@example.org.