White LED W/ 3V or less?
White LEDs are blue LEDs with a phosphor that converts some of the blue light into yellow light that mixes with the blue to form white.

The voltage of an LED is related to the energy of the photons in the light and that energy is dependent on the color.  To make Blue light requires just over 3V.

The voltage requirement for blue LEDs has been going down in recent years but won't ever reach below 3v. The actual voltage of course also varies with the current, which dictates the brightness.  At very low currents (light output) they may be a bit below 3V.

Since you are intending to power the circuit from a 2-cell alkaline battery although it may be slightly greater than 3V when new, it will drop as the battery runs down.  To get a good life out of the battery you should design your circuit to work with just 0.9V per cell, i.e. 1.8V for a 2 cell battery or 2.7V for 3-cell.

As Stefan suggests the best way is to use a switching power supply to convert the battery voltage to that needed by the LED.  Then you will get the best battery life.