What was that about there being lies, dam' lies and statistics? And that was before opinion polls were invented and Eurobarometer was even thought of.
According to the BBC website every member country has a large majority that rather agrees with the Constitution, even Denmark, Ireland, Poland and the UK. Of course, when one starts reading the analysis one realizes that in several countries, notably France, the sailing will be far from plain. Nothing is to be taken for granted on either side.
Still it is a pretty map.