I get the idea that it would be months, which seems untenably long. Maybe the UFP is more dependent on information, which travels faster by subspace radio than ships, but it seems like you couldn't maintain a government if it took a year to traverse it. If the UFP were that big, it would require devoting years to just to visit a distant region. Most people would communicate with those regions but never visit them or exchange significant quantities of goods with them.
I dunno... This is pretty much exactly the model the old British Empire utilized. It would take months to get from England to the American Colonies, even longer to get from England to India and long yet to get to Australia. And all this was without any sort of electronic means of communication and traveling is sailing ships that weren't any faster than your car driving at the legal speed limit though an average neighborhood.
The Brits weren't the only ones to pull this off... The Roman Empire was spread out pretty far also. They could get around by sea a little bit (most of their empire surrounded the Mediterranean) but if you want to get from Rome to, say, Britain, you'll have a very lengthy trip by road. Even if taking a boat along the coast to Gaul (France), Iberia (Spain) or the other direction to Judea (Palestine) or Egypt, you're in for a long haul. This was further limited by weather, the Med is so choppy in the Winter, that the Romans enforced "Mare Invictus" which meant the sea was closed from, like, November to April or something like that. Heck, even in the United States, if you wanted to get from New York to the California coast before there were rail roads, that's a trip of a few months too... one limited by weather... You won't want to try and cross the Rockies in Winter!
There's nothing untenable about a far-flung governmental authority. The British and the Romans both held sway for hundreds of years, so the Federation being spread out and time-consuming to cross doesn't strike me as too hard to swallow...