It will take a while. Many coaches, especially in today's parity-enforced league can have a winning record and/or make the playoffs in a single year. The key is consistency and staying power.
Lovie Smith was fired for going 11-5, 8-8, and then 10-6.
Brad Childress was fired half a season after going 10-6 and then 12-4 with the Vikings.
JG likely came within a hair of getting fired after last season. If he wins the Superbowl he'll be around a long time, otherwise, he's back to fighting for his job like most NFL coaches next season.
In summary if the Cowboy win a couple of playoffs games this season and then go out and have a 6-10 season next year, his job wouldn't and shouldn't be safe.