On macro economic terms a high EUR against USd would ruin ECB's plan to import . On the other hand a high valued USd would harm US economy. This is called an exchange rate tension if not an economic friendly "war" about the exchange rate.
We will have to wait and se. Although on a chartist approach, the pair dosen't look like being able to go beyond 1,0885, we should keep in mind that ECB will put on the table another 60 Bio € . If FEd will come in the market to buy it, this would put EUR up and USD down, but this is not what the market is expecting.