Answering the specific question on whether a day is long enough, I'd say no. If you try and do it all in a day you'll be exhausted and won't have been anywhere long enough to enjoy it. Alternatively, pick one or two highlights and decide whether you'll be needing a return visit after the first trip. We managed to spend over four hours at La Sagrada Familia - we climbed the towers but I'm not sure how the time went so quickly. We're going back to see more in September.