The band open their latest album 'Come Around Sundown' with the track - but with the obvious connotations of its title and lyrics, the other band members were worried singer Caleb may want to end the band.
Guitarist Matthew Followill told Absolute Radio: "I mean, maybe this song was written that way, I don't know, you know, the way Caleb was feeling when he wrote 'this could be the end' or whatever.
"I mean, I took it that way, but then he told me it was about something else, I don't know, he was probably lying.
"Yeah, when he first sang that to us I was thinking 'Okay, yeah, I get it, buddy'."
Despite what the group thought, Caleb had no intentions of breaking up the band - who are now more popular than ever - and most of the words for the album were improvised from his stream of consciousness.
The band are even surprised by the level of success they have reached, and count having won a Grammy award as a career highlight.
Bass player Jared Followill - who, alongside drummer Nathan Followill, completes the band - said: "Winning a Grammy was something that we had never thought that our band would do, that was never one of our goals, and for that to happen it was just like 'Wow'."
Fans can obtain tickets for Kings of Leon's concert in London's Hyde Park on June 30 from Absolute Radio's exclusive presale on Tuesday (02.11.10) at www.absoluteradio.co.uk/tickets.