Ah. From The Phrasefinder site:

From "Morris Dictionary of Word and Phrase Origins":
"welsh -- to anyone with Welsh blood in his or her veins, the old nursery rhyme 'Taffy was a Welshman, Taffy was a thief' is an outrage and a slander. There is no objection to the first statement: 'Taffy' is a generic name for Welshman, a corruption of 'David,' the patron saint of Wales. But we greatly resent the implied slander on an entire nation in the second line...Even worse is the verb 'to welsh,' meaning 'to renege on a bet,'...The term welsher became common in Britain during the eighteenth and nineteenth centuries in the argot of race-track bettors. But from a reader came a comforting word for all Welshmen, one which gives a touch of logic to the use of the term: 'It was ENGLISH bookies who, having too many long shot winners against them, fled over the border to 'boondock' Wales to become the original welshers and escape irate bettors looking for their payoff.'

sian