would i be able to, say, go to the nearest nissan dealer, pick out a model and have it by, say, next monday. At the very latest by next Tuesday?
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Much faster than that.
You could go into the dealer and drive off the lot -- a few hours later -- with the car of your choice. Same applies for purchasing via auto loan.
Some caveats: the interest rate may sting depending upon your credit ranking (if, that is, you choose a hot vehicle, like a Nissan; a dealer for a dying firm, such as Ford, may be more eager to negotiate); also, pay close attention to the mileage terms of any leasing agreement.
I recommend reviewing this advice from Edmunds:
<http://www.edmunds.com/advice/leasing/articles/45858/article.html>
Some more important advice on calculating your potential lease payment:
<http://www.edmunds.com/advice/leasing/articles/48365/article.html>
.d.