Why do you need their letters so soon if you are trying to get your app done by 9/1? Is all your stuff in already? 2 weeks is really the minimum time that one could even possibly expect a letter to get off my desk unless it was an emergency, which this isn't since you want your app ready by 9/1.
People seem to forget that attendings also have a ton of other stuff to do as well, and things get scheduled into a time when I can do it. Making me hurry the letter means that I don't have much time to write you a well thought out letter.
What can you do to help me get it done sooner and still get out a good letter?
1) give me a complete packet of all your info that I will need. that means a CV, an idea of your academic record, a draft personal statement (doesn't have to be final), and if it isn't immediately clear from your personal statement, I need to have an idea of your overall career goals (academics v. not, fellowship thoughts v. not, etc). Ideally, I already know you well enough to talk about you as a person, but if not, I need to meet with you for at least 20-30 minutes to remind myself of your greatest qualities.
2) give me all the paperwork I need to get your letter out (cover sheets with your ERAS number etc).
3) The date that you need it by noted prominently on the packet.
As to getting me to "hurry up" or to meet the deadline (which is really what you want). Having my assistant gently remind me is a good idea if she likes you. A short e-mail about 1 week before the deadline to say hi is ok to let me know that you have all your stuff in already and wanted to make sure I didn't need any more info to get my letter out in time is ok. Stopping by the office on a day that I am in (my assistant can tell you when that is) isn't a terrible idea either. If you know that I'm on service, contriving to bump into me in the hospital isn't a terrible idea either.
I know it's a stressful process for you so you are stressed and yes, attendings do sometimes forget to write the letter at all, so a reminder is not out of the question though. It hurts you much more than it hurts me if I forget, so most attendings are ok with a reminder and won't mind so long as it doesn't come off as demanding. Good luck.