Can I get 2 AA to provide 4+ amp pulses at 5V?
Take a look at the LT3750 Capacitor Charger Controller .  It runs down to 3V, so it would be marginal with 2 alkaline cells, but would certainly run with 3 cells.  Put a high current low dropout regulator like the Microchip MIC29501  on the charged capacitor at the output.  Charge the capacitor up to 6V, turn on the LDO to drive 5V to the output at up to 5A.  You would need something that set the enable pin on the LDO for the desired pulse time.  Between activations, once the capacitor is charged, the current draw would be very small.  Note that you probably want a constant current to drive the IR LED instead of a constant voltage, but that is beyond the scope of the question.