Puzzling Prattle Puzzle

The Puzzle:

Puzzling Prattle

Two school children, who were all tangled up in their reckoning of the days of the week, paused to straighten matters out over a circus poster, when little Priscilla, who was hinting for an invitation to the show, remarked to John; "When the day after tomorrow is yesterday, 'today' will be as far from Sunday as that day was which was 'today' when the day before yesterday was 'tomorrow'"!

On what day of the week did this puzzling prattle occur?

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