DUBLIN—Ladbrokes in downtown Dublin was paying one to 33 that Irish voters would approve Europe's Lisbon Treaty, against eight to one that they would strike it down. For non-gamblers, that means the betting chain thought the EU charter was a favorite to win—by a lot.

Two doors down, patrons of the Sackville Lounge turned away from televised horse races to reveal why. After Irish voters spurned the treaty in a referendum last year, the European Commission—the EU's unelected legislative, regulatory and executive branch whose...