The Capital One Cup winners trail the Blaugrana 2-0 going into the second leg but the Liga champions were beaten on Saturday and could be vulnerable
While Lionel Messi opened the scoring from the penalty spot, having been fouled by Demichelis, it was Dani Alves who struck the hammer blow in stoppage time to hand City an almighty task to progress.
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Yet the Catalan giants head into Wednesday's game off the back of a surprise La Liga defeat to struggling Real Valladolid, which put a major dent in their domestic title ambitions.
The 1-0 loss at the Estadio Municipal Jose Zorrilla leaves Barca four points behind leaders Real Madrid ahead of the crucial Clasico towards the end of the month.
While Barca have been below their best since winning in Manchester, Manuel Pellegrini's men have endured mixed fortunes.
The Chilean picked up his first trophy as City boss with victory over Sunderland in the League Cup before his side crashed out of the FA Cup on Sunday at the hands of old foes Wigan Athletic.