What's the big rush to get this flight away? Are we at war? Is there a medical emergency?
Sit on your hands, make some radio calls, keep the pax / crew informed ( there goes 3 minutes) , realise that the sun will still come up if it takes an hour or two to arrive at an engineering fix ( probably different tug or deplaning) and then chuckle to yourself about the story you'l tell on your next overnight.
All you folk who want to rev it up to keep on schedule sure must think your individual flights are critical.