I actually sent off my letters of rec 3 weeks after I turned in my primary. I was thinking the Pre-prof office here at UCLA would take three weeks to actually process the letters after I turned in the request then send them off, but it took them 3 days. And not a single school threw away my letters of rec. I did call and check that every school got them, though. Of course, I didn't send the letters to the UC's, Michigan and NYu yet because I knew those schools specifically tell you not to send them in until they ask for them.
What you should be doing right now is filling out secondary questions from last year. I posted somewhere on here (Foxy???) a list of a lot of the questions from last year that you could work on. That way you would have a quick turnaround time with the letters.