I don't think that a week is enough time for them. And even if it is, they might be a little annoyed and not prepare the best possible letter for you.
One of my recommenders was quick, efficient, and organized. She asked about my academic history, my future academic and professional aspirations, and other topics in order to write a good letter. The other recommender wrote a "he's the best" letter and it was somewhat vague. While I appreciate his efforts, some admissions officers probably found it insincere and ultimately unconvincing. It also took me months to get that letter.
My advice to you is find someone who knows you well enough to write a reliable recommendation. And most importantly, be structured and actively pursue this. Don't be passive and say, "oh, just hand it in when you're ready." Give them a clearly defined timetable and occasionaly check on their progress (without being too stuffy). You can't write the letter for them, but you can give them ideas. Tell them what the letter could include and organize what you have to say at this time. And make sure they don't write a "he's perfect" letter.
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