Edit30 has a two-part analysis of how Hyatt has shot its brand in the foot, and what Hyatt's communications consultants might try next. However, in this case the simplest recommendation is the best: Hyatt should apologize and rehire those housekeepers.
Part 1 - Hyatt PR gaffe goes viral, global
Part 2 - Hyatt: Managing the Boston aftermath
From the article (pt 2):
"Then, of course, there is the issue of addressing employees’ concerns and bolstering morale. The “they’re just employees” attitude won’t cut it, especially now. This is a serious area in which Hyatt has previously fallen short, in Boston as well as elsewhere."