The patter is believed to have been derived from 'Shi-ga-tsuyo-katta' in their Edo accent, which can be heard as 'Shigatsu-yokka (April 8),' which is Buddha's birthday.
江戸っ子訛りで「しがつよかった（火が強かった）」＝「四月八日だ」＝釈迦の誕生日、というつながりで成立したとされる。