You may have been referring to this, though:
In 2003, Carter started every game, and the Cowboys went 10-6 and lost in the first round of the playoffs. In a stunning move, the Cowboys released Carter in training camp in 2004 after he reportedly failed a drug test. That left 40-year-old Vinny Testaverde, whom the Cowboys signed in free agency, as the starter, Drew Henson as the backup and Romo as the third QB. Testaverde lasted only one season, and the Cowboys went 6-10.
In 2005, the Cowboys signed 33-year-old Drew Bledsoe, who had been to a Super Bowl under Parcells with the New England Patriots, after the Buffalo Bills released him. Romo was elevated to the backup spot, and Henson was the third QB. Bledsoe started every game, and the Cowboys went 9-7 and missed the playoffs.
Romo improved each preseason, combining for 47-of-76 passing for 523 yards with two touchdowns and two interceptions. On one memorable play in 2004, Romo led the Cowboys to a come-from-behind win over the Oakland Raiders after running a quarterback sneak for a touchdown with just six seconds remaining in the game. He had disobeyed Parcells, who wanted a different play. "We're kind of happy he scored, but Bill is mad," Payton said. There were rumblings that Romo was on the roster bubble.