I'm kind of guessing this device is intended as some sort of prank. It's going to be tough not to drain small batteries in a week, just using the timer portion. I just know enough about microcontrollers (AVR) to program basic stuff, still struggling to get control over the more advanced features. I do know that when the MCU goes into Power-Down Sleep mode, almost all functions are shut down until an external interupt wakes it up. Maybe somebody else knows if you can use the 'Sleep' instruction for a set period.
Most microcontrollers don't seem to burn up a lot of power, it's mostly what you are driving. ATTiny13L at 1 MHz, 1.8 volts, draws 240 uA in active mode. The internal clock can be set as low as 16 kHz (128/8), so guessing much lower current draw.
Clearer details would make it so much simpler to giver better solutions. This is kind of a 'unique' application, most likely won't find anyone who has done this before, so the more you put into your request, the more likely somebody here will respond with a useful solution.