I will be studying in Spain for 81 days, then a break for 3 weeks, then to the UK to study another quarter. I leave in a week and never got a Schengen Visa because my second quarter plans came last-minute. The UK is not a schengen country, but would need a visa for travel over 8 days total outside the UK later to any other Schengen country. Suggestions for getting a schengen Visa this late in the game? Or will I not be able to visit France or Spain (again) during my second quarter (81 days) in the UK?
I'm not completely understand your travel plan as well, but based on my experience on getting lots of Schengen visa. It usually took me about at most 3 days to get the visa, but that means you're well prepared with all the documents they need. I'm not sure what's your nationality because there's a huge difference in terms of getting a visa for certain nationalities. Also, if you're studying in the UK and want to travel to Schengen area and back to the UK again you need to have at least 3 months left on your UK visa. Otherwise, you need to show an already paid for return ticket to your home country.
Also from my experience the pain is not getting the visa, the pain is to get the appointment. Sometime if you really want it you might need to pay an agency to get the place for you.
As I am a citizen from one of the Schengen area member states, I have no personal experience to share and I don't know how well it works in practice but the Schengen visa code specifies that you should receive an answer within 15 days of your application so there are certainly no guarantees you can get your visa in a week. Best to contact the relevant consulate as quickly as possible.
Also, I am not sure I completely understand your travel plans but quick visa or not, you need to make sure that you are not going to fall foul of the 90 days in a 180 days period rule otherwise you could face serious trouble (be refused entry and have difficulties when applying for a visa in the future).
As far as my experience with this matter tells me, you need at least 14 days for a Schengen Visa to be issued.
And since you might be leaving the Schengen area and wanna come back in, you must request a 2 entry visa supported with travel and accommodation reservations for all destinations, otherwise only one entry will be granted.