I really see no reason why they couldn't do a flash one day strike to give the NYers a taste of what's to come and then as a goodwill gesture agree to work until the weather gets bearable or enought time for the general populace to think of alternatives and then go for an indefinite strike if negotiations don't get better.  I think Renee in Ohio's diary makes a good point on the fat in the MTA management. What I object to is the timing of this strike. They will  still have leverage because a strike at any time will inconvenience the city. Just don't go over the top by insisting on doing it now, right during the middle of the winter. MTA management may suck, but the drivers still serve the public on its own dime and the MTA employees do get slack in their work performance. It's not like they are held to private corporation standards. So they should be a little flexible with the timing.

I worked at UPS when they had that major strike around 1997. Even after the deadline  expired, the unions gave extensions to find a way to keep working while negotiating.

FWIW, I do fault the MTA management primarily for this crisis. I do find the NY law over the top. You gotta let the employees strike, otherwise you give them no leverage at all.  I don't see why MTA management is not running a barebones skeletal crew to transport the really desperate passengers who are willing to bear the long wait lines for a train. UPS management did that when the drivers went on strike.