If any signals from the ECB remain relatively hawkish because the doves on the council continue to receive less attention than the hawks, EUR/USD might well return above the 1.11 mark. 

Only once the ECB’s interest rates have peaked too and when it becomes clear that it is not doing enough against price pressure because of the peripheral countries even though inflation remains stubbornly high, a risk premium for the Euro will become justified. That will take a while though, so that short-term the EUR is likely to appreciate against the Dollar.