Can anyone explain how the total energy of the Universe might be zero, or nearly zero?

Answer 1

Basically, it has to do with opposites. Every particle of matter has an opposite particle of antimatter. When these two come in contact, they annihilate eachother.

If every particle of matter were to find it's specific particle of antimatter, the universe would cease to exist. Theoretically.

Answer 2

Einstein had suggested that there was an cosmological constant, or some sort of balance force in the universe that held it stable. first he said that it was his greatest blunder, then he called it his greatest discovery, much later. the energy of the universe may not be zero, it's ambient power radiating neutrally in a 'off' state in the empty space between solid objects, but before he died , Einstein did suggest that this power was , in some way or state, accessible to us, assuming we have the intelligence to learn to do so.I believe we do.