Some friends speaking to me after launching this website were positively surprised about “this great and fresh idea”. I say: thanks for the credit but our only achievment really is re-activating an argument from the Convention.
It was apparently a French (+ others) idea to install a permanent president of the European Council. These intergovernmentalist forces – joined by few other less ambitious member states and MEPs – had the intention to bring about a completely new institutional order with the abolishment or radical weakening of the Commission President. This would have been achieved by installing a strong and permanent European Council (EC) president. The Convention Presidium took up this idea of a permanent president in its drafts of late spring 2003.
However, Giscard and friends were experienced enough to propose an arrangement that somehow cares for a potentially more useful division of tasks between the EC and Commission president. In their draft of late May 2003 they actually foresaw the opportunity for Commission and EC president to be identical (the so-called “big double-hat” – as opposed to the “small double-hat” being Vice-President of Commission and Mr/s CFSP of the Council). The French accepted this compromise arrangement then (securing an EC president) while in return the grouping of small member states accepted to have a rotating system for Commission members in which there was guaranteed pre-allocation for big member states.
A funny note on the side comes from then German foreign minister Joschka Fischer. When asked about the double heading (EC and Commission president) he replied that he has only good experience with “Doppelspitzen” in his own party 
Another interesting piece from the l’armoire de l’histoire or the birth of the idea – the idea and/or its tabling was a joint venture of Chirac and Blair in the first days of the Convention. After Aznar stepped in to support their genious, the idea soon became known as the “ABC Proposal” (Aznar-Blair-Chirac).
Berlusconi and Schröder were the next ones on board, and of course the European Council’s founding father Giscard, who soon became the leading crusader for the establishment of this new institutional figure, as he saw in it a kind of reincarnation of his old idea – and of course a tailor-made position for himself as the first incumbent to be inaugurated to the throne…
I thought the idea was actually coming from the Brits, ahead of the Convention. See the FT 21 January 2002 “UK wants EU ‘super council’: Radical plan would recognise the importance of Europe’s big three powers,” Apparently Blair wanted the creation of the post of “permanent secretary general to chair Council meetings” which would have ended the rotation of the presidencies. Where things got out of control was that the plan also proposed the creation of a ‘super Council’ composed of the Big Three, taking decisions without the other Member States… Belgium and Ireland loved the idea. Anyway, no wonders why Blair wants the job: he taillored it for himself.