| I'm studying in France and have had the same consulate issues...they tend to only be responsive if you go to the physical office, dress up and politely ask your question.
Anyways, at least for France (which is probably similar in terms of visa requirements) you MUST get your student visa while you are in the states, and you have to appear in person to get the visa. But, I just went to the website for the spanish consulate and it says that long stay student visas (which you will need as you are staying more than 3 months) can be applied for "as early as three months in advance or earlier." Is it the exchange organization that says you can only get the visa 90 days before the program? Or will the consulate accept visa applications more than 3 months in advance, but not issue visas until the 90-day-or-less period? If this is the case, would it be possible to delay your departure for a week or so (you said that you wanted to be an au pair for June, July, August, barely over 90 days)? Otherwise, the only option I could see would be to return to the states to get your visa.
Could a representative from your study abroad organization help you?
Edited to add: also, when I showed up at the consulate for my visa application, it turned out that basically all of the information on the website was outdated, and that I had hundreds of pages of documents that were no longer required and was missing some new key forms. So basically, the visa process sucks, and the best way to straighten the whole thing out is to go in person. | 
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