It depends on Romo's recovery time and the Cowboys' performance while backup Jon Kitna fills in as the starter.
Romo is expected to miss six to eight weeks with a broken left collarbone suffered when New York Giants linebacker Michael Boley hit him during Monday night's loss. It's likely the 1-5 Cowboys will be eliminated from playoff contention by the time Romo is ready to return.
If that's the case, the Cowboys would weigh the risks of Romo playing against the potential rewards of the Cowboys finishing strong.
"We'll just see what the circumstances are at that time," Jones said Thursday after a North Texas Super Bowl committee event at Cowboys Stadium. "We'll see how well we're playing. They remember what you do in November. That is an old college saying that my coach used to say all the time.
"If we have an opportunity to have a good taste by the team playing well, have a good taste in our mouths ... then even if you're out of an opportunity to be in the playoffs, you want to be playing good."
If it takes Romo eight weeks to recover -- the most likely scenario, according to sources -- then he wouldn't be ready to play until the Dec. 19 home game against the Washington Redskins or the Christmas road game against the Arizona Cardinals.
"I wouldn't be presumptuous enough to know how fast he's going to heal," Jones said. "The faster he heals, the better I like it. We will be weighing that aspect of where he is in the healing process relative to any risk that you might take with him playing."
Jones expressed confidence in Kitna, although he acknowledged he can't know if Kitna can still be a capable starter until it happens. Kitna hadn't taken a regular-season snap since October 2008 with the Detroit Lions before Romo was injured during the second quarter Monday night.
The Cowboys' offense sputtered with Kitna, going three-and-out on six consecutive possessions. Kitna finished the game 16-of-33 passing for 187 yards and two touchdown passes to rookie receiver Dez Bryant, both of which came in the final four minutes of a game the Giants led by 18 points in the fourth quarter.
Jones does not believe it's in the Cowboys' best interest to focus on evaluating young players, such as starting second-year quarterback Stephen McGee instead of Kitna.
"I think we should use everything we've got on every play to win every down," Jones said. "It's important to this team every time we get a chance to win within the context of the game or in the context of the possession. We would not, in any way, compromise a chance to win the game by playing a player to evaluate or to give him experience."