Deiseach, that would be the conventional wisdom, run the ball and keep running until you are in fieldgoal range, or else dump off a couple of 5 yard passes and try to get a few yards after the catch (YAC). I don't know if this was a long bomb or a big run after the catch.
The other thing is that the defence nearly always expects run or short pass in overtime, and if they do, then they usually play their 2 safeties up to put at least 8 or 9 men 'in the box' which is the area just behind the line of scrimmage. It's traditional run stopping practice. If they do that, then it's usually 1 on 1 outside, and no QB worth his salt will throw an INT in 1 on 1 coverage. Usually interceptions are because the ball is tipped, or else a Safety or Linebacker is anticipating pass and either gets in the way, or goes double teaming the receiver.
If they are expecting run, and Favre does a play action fake, i.e. pretending to hand the ball to a runner before spinning around to throw, the chances of a big play, especially in those circumstances, are much greater, and the chances of an INT goes down as well.
So, without seeing it, I would reckon it was a defence playing run, a good play action fake to suck the safeties in further, and a long pass to a single coverage, or wide open receiver. That's what I'd do