Before you get the wrong idea, the fixing is for the building, not the government (that's something else entirely). The city wants to make some improvements to City Hall and will spend $60 million to renovate the building and bring it up to speed.
The Post reported that commissioner of the Department of Citywide Services spoke to lawmakers on Thursday about the problems with City Hal. Martha Hirst said, "We have found exposed electrical wiring in the underground basement tunnel, which can endanger those who undertake repair work... Some of the needs precipitating these repairs, such as structural deterioration under the limestone steps or the piecemeal network of fire alarms...may be invisible to the everyday observer except when an incident occurs." She also mentioned that visitors get stuck in the elevators for up to an hour, which could be a "serious problem" if it coincides with a medical problem. It seems like City Council members and the Mayor want the work done, as there's already $27 million allocated for repairs in this year's budget.
The incarnation of City Hall we know today was built between 1803 and 1812, by Francois Mangin and John McComb Jr. (The first City Hall was on Pearl Street; the second was on Wall and Nassau Streets.) According to the City's website, it was "designed the building in the Federal style, with clear French influences that can be seen in the large arched windows, delicate ornamental swags, and more decorative Corinthian- and Ionic-style columns and pilasters." You can call 311 to arrange for a free tour of City Hall. And a fun fact via Wikipedia, City Hall is mentioned in an Irish folk song, the Irish Rover.
Beautiful photograph of City Hall by wallyg on Flickr