The source told the BBC's Jon Sopel that during the leaders' conversation last night, the tone went "downhill" at the mention of resignation.
It was claimed Mr Brown's approach was to begin "a diatribe" and "a rant" and the source said the Labour leader was "threatening in his approach to Nick Clegg".
Mr Clegg was said to have came off the phone assured that it would be impossible to work with Brown because of his attitude towards working with other people.
Both parties are now denying it - but they would, wouldn't they? The question of the hour is how strongly Clegg will insist on electoral reform as a condition for a new government with the Tories. And that is affected by the strongly democratic nature of Liberal Democratic politics. Clegg cannot get too far in front of his party. Meanwhile, #dontdoitnick (i.e. don't surrender on proportional representation) is rising on Twitter and an unruly crowd has assembled in London to demand electoral reform. Rick Hertzberg needs to get on a plane soon, don't you think?