The US embassy site ( http://madrid.usembassy.gov/citizen-services/faq-spain.html ) states that since the US does not have an agreement with Spain, you have to take the driving test (theoretical and practical, or maybe just one, I have no idea as I don't live in Spain, but a compulsory medical test also for those who just exchange the license is mentioned) and go through the usual bureaucratic process to get a Spanish driving license.
Also the DGT website (warning: I speak Italian and not Spanish, but I checked my understanding of the Spanish text with google translator and it matches), under the section dedicated to permit exchange: https://sede.dgt.gob.es/es/tramites-y-multas/permiso-de-conduccion/canje-de-permisos/
has a section dedicated to each situation that allows you to exchange your license, with PDFs available also in English.
The situations listed are:
Exchange for permits acquired in EU/EEA
Exchange for permits acquired in non-comunitarian countries (Andorra, Korea, Japan, Switzerland and Monaco)
Exchange of permits obtained in countries with agreements
and then other stuff that is not relevant for you unless you're a diplomat or can prove you're a professional driver.
The US do not appear anywhere, and all the texts under those sections mention an "agreement" (basically licenses need to have been obtained after the agreements).
If the US were anywhere to be found, it would appear in 2. along with those countries, which by the way aren't mentioned in the list of countries with agreements (but I guess there is an agreement since it's just them and not others, plus the PDF with the instructions mentions the agreement), so the website is pretty weird.
The IDP is valid for 1 year, but that doesn't stop Spain from requiring that you obtain/convert the permit within 6 months. The IDP is just a translation of your US license. It's not like your US license goes bad if you live in Spain either. All countries do this AFAIK.
Upon further resesarch in Spanish on the internet, I found other people complaining about the US or other countries not being mentioned at all, and people asking about this. Usually it ends with someone saying your need to take at least an exam...
I guess you should start to learn Spanish ASAP and ask the institutions directly and then proceed, and/or find a driving school specialized on expats that can help you pass the exam without actually learning a decent level of spanish (but I bet they'll make you pay a lot more for it than standard schools).