Actually there was some bad press. According to the book Iwo Jima by Richard F. Newcomb, Page 202: (which I happen to have here on my bookshelf at work,) on February 27 the San Francisco Examiner, in a front-page editorial said that although victory was certain, "there is awesome evidence in the situation that the attacking American forces are paying heavily for the island, perhaps too heavily."
It went on to say that if Gen MacArthur was in charge of this campaign, more men's lives would have been saved. It also asked the question, "Why do we not use him more, and indeed, why do we not give him supreme command in the Pacific war."
Of course it can be pointed out that this editorial was more about MacArthur and Nimitz than about American lives but there is no doubt it caused a fire storm. Some Marines stormed the paper offices and demanded an apology from the editor, which they did not get. Police were called but the Marines were not charged.
After initial negative response from casualty reports, Nimitz kept them from the press until the end and then referred to them only as a fraction of the enemy’s losses.
It's easy to see from our view point looking back through history how necessary taking the island was, but there was a lot of anxiety at home concerning Iwo and the reaction was not always positive.
In any event, I think the parody was ridiculous because you can't compare today's political and military environment to 1945. If we were in a world wide campaign the scope of WWII right now, I can guarantee the majority of the press would not sound like cutie. We may not be able to live up to the greatest generation who ever lived, but I don't think we have sunk that far yet.
Thanks for the link though, I've added many nice Iwo pictures to my collection from it.