I believe it is 30 days.
If your Broker submitted the paperwork electronically it's conceivable it actually can be acted on within just a few days (if they want to do so).
Given that you haven't heard anything in a 6 week time frame you may want to contact Marriott directly to confirm what exactly is happening. Your Broker should be all over this so I am surprised she hasn't contacted Marriott herself.
I think the odds that Marriott would act on it (i.e. take it back) is highly unlikely UNLESS it is a week 52. How much did you offer and what exactly are you trying to buy (i.e. one, two, or three bedroom, every year or every other year, and when is your usage supposed to begin) ?
.