Simple, efficient "breathing" LED circuit
A CR2032 has a capcity of ~ 200mAH. For 2 weeks, this gives you an average current budget of ~ 500 uA. A plain 555 has a supply current of a few mA, so you'll need to use a cmos 555, which has a supply current of (max, @ 5V) 250uA. Use the highest value you can use for the timing resistor.

Assuming your LED current is 2mA, and the LED is on for 3/10 of a second, the LED will add an average of 200 uA. That brings the total to 450 uA, which makes your idea just about feasible. But forget the 'generic' 555, and a high-efficiency LED would be a better idea than your generic 20mA LED. Also don't go for a bargain-quality battery.

Reducing the LED on-time will make a big difference, as would using a well-programmed microcontroller. Or a fatter battery.