What happens if I need to burn 3 but only have 2 cards in my main deck?

Yes — you burn as many as possible, Burn Out, then finish the burn.

Sequence: burn the 2 cards you have, then perform a Burn Out (recycle your Trash into your Main Deck, randomize, and choose an opponent to gain 1 point), then burn the remaining 1 card from the recycled deck to complete the "Burn 3." This applies when Burning is part of an effect; the same interruption-and-continue structure applies to Draw (Rule 431.1.b, 440.4).