Calculate output voltage and current of a boost converter
There's the Law. The Laws of Thermodynamics, to be precise. One of the things following from them is that you can't create energy out of nothing. So you'll have to do it with the energy stored in the batteries. Energy is power x time, and for the batteries that will be 

\$ U = 2 \times 1.2 V \times 2000 mAh = 4800 mWh \$

So if your switcher has a 100 % efficiency you should be able to get

\$ \dfrac{4800 mWh}{5 V} = 960 mAh \$

from it. Forget 100 % efficiency, 85 % will be nice. So that's 15 % less, or 816 mAh. It's up to you how to use that. If your device uses 10 mA you can power it for 81 hours, that's more than 3 days continuously. If it needs 100 mA the batteries will be gone in 8 hours.