You have a finite amount of energy in the two battery cells. The joule thief concept works by maintaining a constant output voltage.
Typical AA battery cells contain 2700mAh (milliamp hours) of electricity. This means you could drain 2.7 amps out of a single cell for one hour, or 5.4 amps out of a single cell for half an hour. Realistically, the current draw will be limited by the physics of the cell.