How Much Current is Usually Used with IR Transmitting LEDs, in Remote Controls?
They typically have something like 10-50 ohms in series with one or two parallel LEDs and a driver transistor or MOSFET. 

Assuming a 2.5-3V battery voltage (2 AA or AAA) and a 1.2V LED voltage that's maybe 20 to 200mA. 

I had a remote that I extended the range on (for a bedroom remote where the IR light had to bounce to get to the set-top box at the back of the lift), and I did it by replacing the LED with a more efficient type rather than by jacking up the LED current.