The US Open has gone into a third week pretty much without fail in recent years. But I don't recall that happening with a final part-way completed, it's always been postponed to the Monday and the complete match played on one day. Likewise, the 2001 Ivanisevic-Rafter Wimbldeon Final started and finished on the 3rd Monday.
The last Slam Final that was threatened with this was the 2008 Nadal-Federer Wimbledon classic. The ref said after it that the 16th game of the deciding set would have been the last for the evening, even if the scoreline had been 8-8 instead of 9-7. But that won't happen again due to the roof. Although the day of the Men's Final could still slip, if the weather is really horrendous and Centre Court is the only possible venue for matches for a number of days.
So, in summary; dunno, sorry.
Edit - I've now looked it up, and the
last four US Open Men's Finals have been played on Mondays. That really is getting to be a serious issue. I remember some talk about this during last years tournament (understandably), and that was along the lines that given the design of the Arthur Ashe court, which is a vast and open bowl-like structure, it would be very difficult to modify to include a roof.
Looking at the image, I can see what they mean. The USTA need to spend some money on this...
The French Federation would appear to have similar issues with Philippe Chatrier, but apparently a roof is due in 2017