With 200GB of data, I'm assuming you have a bunch of very large files. Something like multiple 10-20GB video files. If that is true, then the time calculations are not accurate because USB2's throughput is too inconsistent. On paper, USB2 has a burst speed of 480Mbps, but often can't maintain that speed over long periods of time. But Windows and OSX's time calculations assume "average copying" of small files and can't correctly calculate when a large file is copied. They see how many "files per second" are being copied, so when it takes several minutes for just one large file, the OS thinks that the copy is slowing down, when in fact the same bits-per-second is happening.
That said, my experience a while ago when copying a single 25GB file, it took 40min using Firewire400 versus 2.5hrs over USB2 to the same hard drive. (The drive had both Firewire and USB2.) You can see why Firewire is usually recommended for transfering large amounts of data. So to improve, definitely replace the USB drive with a Firewire one. I believe your Mac has a Firewire800 port so a 25GB file would be less than the 40min it took with my Firewire400 drive.
So for 200GB of data, my benchmark infers something around 8 hours over USB2. My experience is that USB2 "chokes" when copying for that long so it may take a little more time than that. I mentioned that USB2 can't maintain it's maximum speed over long periods of time. What that means is that some data packets don't copy over correctly and the USB protcol has the packet sent again, which means it actually sends much more than 200GB, in your case. Therefore 8-10 hours would not be unreasonable IMO.
And realize that the calculations you're seeing are for Time Machine, which also has to index/catalog all those files after it's done copy, which obviously will take additional time. Probably not 14 nor 26 days, but using a USB2 drive for Time Machine, definitely overnight at a minimum.