A few things come to mind when I think of the Jenga tower:
1) When the tower pitches over, that's it. The end result is something catastrophic and final. For a D&D game, you would need to include a powerful and irreversible consequence to reaching the end of the line, whether it be a curse, or one or more PCs' deaths.
2) The worsening situation is obvious. You can see that there aren't many blocks left to remove, and the tower gets a little more wobbly as time goes on.
3) You know things are getting worse in Jenga, but you never know how close to the end you are. The structure might look like it can take three or four more block removals, but the next one just might send everything tumbling due to an unsteady hand.
In 4e, I'd run a modified skill challenge, something like: find the secret counterspell to the curse before the demon awakens (and the party meets a Very Bad Ending). I'd make it complex, with a high DC for most checks. That satisfies the first consideration above.
Instead of the standard three failures, though, have something like six, but every time a skill check is failed, roll a d4 and add that many failures to the count. That way you might have six chances to recover from failure, or only two, but if your first roll is a three, you have no way of knowing whether or not the next mis-step will be your last...and that should give your players reason for worry. Just be sure to give them ample opportunities to use secondary skills, and consider giving automatic successes for clever actions that the players suggest (which goes for regular skill challenges as well, I'd think).