Crayton was hurt in the first quarter on Sunday against Washington, but didn't miss much time, still catching two passes and returning punts. His ankle was still sore Monday and bad enough Tuesday that he didn't work out, even though coach Wade Phillips described the practice as being not very strenuous.
"I'm worried that he may not be able to play," Phillips said. "With the game coming this quickly, it could be a problem. I think if this was a normal week, he probably would be fine. It's going to be kind of back-and-forth as to whether he'll be ready for Thursday."
Playing opposite Terrell Owens, in the role vacated by injured Terry Glenn, Crayton has caught 31 passes for 466 yards and five touchdowns this season. If he is inactive, second-year receiver Sam Hurd would take his place. Hurd has eight catches for 141 yards and a touchdown.
"He's played well every time he has gone in for us," Phillips said. "If he has to start, we have confidence in him playing and doing a good job."
Cornerback Terence Newman would replace Crayton on punt returns.
With the Jets 2-8, the Cowboys might be tempted to rest Crayton to make sure he's back to full speed for the following game, against NFC co-leader Green Bay a week from Thursday.
"In a short week like this, you've got to be careful," Phillips said. "You've got to look at long term as well as short term. The difference is, the guy got a sprained ankle in the game, was real sore yesterday and couldn't practice today, two days before the game."