For most of its history the USA did, in fact, operate as what we today would consider a libertarian country. All things are relative in politics, and our government (especially the federal government) used to be much smaller and less intrusive than it is now. It wasn't perfect by any means, but it did by-and-large work.
How would fire departments and libraries run in a libertarian country? The same way they do now, I guess, since those are examples of functions that haven't generally been taken over by big government -- yet. But we could do without the enormous social entitlement programs and global high-tech military presence that we've been taxing and borrowing like mad to support.
Franky, it really chaps my hide when I mention libertarianism or mention the Tea Party and then somebody comes back with, "OMG you want to get rid of public schools, public highways, libraries, fire departments, police, etc!" What the hell? Where do they get that from?