The Cowboys can clinch their 18th division title since 1970 by winning their last two games.
They are in that position despite losing five games by a total of 20 points, but there is also one lopsided blemish, a 34-7 loss nearly two months ago at Philadelphia, the team the Cowboys (8-6) play in their regular-season home finale Saturday.
"There is obviously a thrill to dream about what can be out here, the success," Jones said this week. "But I'm also, because it is the Eagles, after the butt-kicking they gave us up in Philadelphia, I'm scared."
Jones probably also remembers the 2008 season finale the Cowboys lost 44-6 at Philadelphia to miss the play-offs.
But the Cowboys owner is often overly optimistic, leading to the idea that he is using a psychological ploy against the Eagles.
"It's probably not my position to explain that," said Jason Garrett, the Cowboys coach. "I know that we, as coaches and players, are focused on getting ready to play our best … We have great respect for their team. I think everybody is excited about the challenge."
Like their coach, the Cowboys do not seem worried about the owner's "scared" comment.
"We obviously took a tough loss to the Eagles last time, so we know this team is dangerous," said Tony Romo, the quarterback. "We have to play a great game out here to get a win. I know we've approached it that way. We're excited about going and playing those guys."
The Eagles (6-8) still have a chance to win the NFC East and get to the play-offs, but they must win their final two and get some help.
That would include the New York Giants (7-7) losing their game earlier Saturday against the New York Jets. If the Giants win, Philadelphia would be eliminated from the play-offs even before kick-off at Cowboys Stadium, which could alter the dynamic of the game.
Until then there seems to a sense of uneasy anticipation for Jones.
"I have that kind of feeling about the respect turns into being afraid of what they can do to you if you have some breakdowns out there," he said during a radio interview. "You can put that 'scared' in there if you want to. I think sometimes I do the best when I'm scared."
If the Cowboys had won some of those close games, most of which they led late, they might already have wrapped up a play-offs spot.
"You can't really concentrate on that," said Sam Lee, the linebaker. "When you have a team like the Eagles coming in, you better be focused. Or it could be another night like it was last time."