It's not because of that one playoff win. If Romo wins one playoff game and loses the next, the pressure will not be off of him. Ask Danny White.
What means a great deal is the Cowboys are a high profile, high pressure, highly scrutinzed team with expectations to win. The Saints are a lovable loser franchise who are a feel good story.
So if Romo chokes away his team's chance at the playoffs the way Brees did last year in the Tampa Bay and Chicago games, it's the feature story on Sportscenter every night ... not swept under the rug. And if the Cowboys were sputtering as badly as the Saints currently are after a great first half of the season, it's "OHMGZZ THE COWBOYS ARE CHOKING!!" not "Oh well, the Saints have nothing to play for so it's not a big deal."