You are talking about the Vf of the LED which is how much voltage will be measured across it when it is on. Generally when you say something "draws" this or that we are talking about current not voltage. Nitpicker, nitpicker..
The Vf of an LED varies with color and the chemistry can have an affect also. Red are typically around 1.9 - 2, green 2.3 - 3 depending on type and blues 3v and up.