This is currently no solution to place a cap on how much money can be spent within some specified timeframe (e.g., 1 day/week/month) when using MTurk with AWS billing activated.
Here’s what I found: https://www.mturk.com/help
It doesn’t really say that you can place a spending cap on the account. The thing is, if you post a HIT, you have to be able to pay the workers, so it looks like it’s a matter of limiting the number of HITs you post or limit the amount you spend on a HIT.
If you don’t approve HITs and authorize payment within 30 days, they are automatically paid. If you put a spending cap on your AWS billing and there isn’t enough to pay for the HITs, that would cause problems with MTurk.