Xjyuk

I was told once about a story in which there was a toddler with god-like powers. The story dealt with the difficulties that the adults around the toddler had with the fact that they could die from a tantrum.

I don't know much about it, but the premise seems quite interesting. I'd be very interested in finding it.

That sounds like "It's a Good Life" by Jerome Bixby.

http://www.isfdb.org/cgi-bin/title.cgi?411091

Adaptations

"It's a Good Life" (The Twilight Zone), an episode of the 1959 TV series

"It's a Good Life", the third segment; a remake of the Twilight Zone episode "It's a Good Life" in Twilight Zone: The Movie (1983)

"Bart's Nightmare – "Treehouse of Horror II" – The Simpsons (1991)

"It's Still a Good Life", the 31st episode of The Twilight Zone (2002 TV series) which acts as a sequel to the episode in the 1959 tv series, with certain actors reprising roles from the original episode.

"Johnny Real Good", from the 12th episode of the first season of Johnny Bravo which stands more as a parody of the Twilight Zone episode. Johnny must babysit a boy with god-like powers who constantly sends him to a corn field for thinking bad thoughts.

That's "It's a GOOD Life" by Jerome Bixby. It's a classic story -- after the tantrum is over, the bodies wind up buried in the corn field...

Here's a Wikipedia page which discusses it.

It could be "When the Bough Breaks" a 1944 story by "Lewis Padgett", the joint pseudonym of Henry Kuttner and C. L. Moore.

Physicist Joe Calderon and his wife Myra have a baby son, Alexander. Four little dwarves with oversized heads begin visiting them to train Alexander--Alexander, his parents are told, is the first specimen of Homo Superior, and is still alive in the year 2450, from whence they have come. When Myra and Joe try to interfere the dwarves use a paralysis ray on them, and try to console them by telling them they are worshiped in the twenty-fifth century.

In a month the infant has a bigger vocabulary than his parents and when he wants candy he just teleports mom to and from the store. He develops a cruel and callous sense of humor, and uses his superpowers to play jokes on his parents (shocking them with electricity, for example.) The ending took me by surprise. Because Alexander is invincible it is impossible to discipline him. The dwarves had warned him to be careful with one of the training devices they brought with them from the future, but Alexander ignores their advice and immolates himself.