The show seemed to be doomed by unreasonable expectations almost from the beginning. People kept drawing comparisons between it and The West Wing, which practically set it up to fail, since this show couldn't hope to follow in the same thematic footsteps. The inner workings of Hollywood don't present the same challenges as being President of the United States does, and doesn't present issues that concern everyone the way a political show does. Likewise, the focus on a more character-driven elements (especially by putting a couple with a turbulent romance up front) shocked people who were expecting it to be as plot-driven as its predecessor.
Studio 60 is a good show, but like a rookie comedian trying to perform a follow-up act after a big name, it just had the deck stacked against it.