After I shrunk the volume in Windows by a disappointing amount, the option to shrink the volume in the Fedora 20 installer became available allowing me to shrink it down by much more.
Shrink the volume in Windows
1. Boot into Windows
2. Go to "Disk Management"
a. Right click "Computer" from the desktop or Start Menu
b. Click on "Manage"
c. On the left pane, click on "Disk Management"
3. Shrink your Windows volume
a. Right click on the volume "OS (C:)" in the top or bottom pane
b. Click on "Shrink Volume..."
c. Enter the amount you want to shrink the volume by
i. If you are allowed to shrink it by the desired amount, congratulations, you're almost done
ii. If not, leave the value alone and we will shrink it down further later
d. Click the "Shrink" button
Shrink the volume again in the Fedora installer
By shrinking the volume first in Windows, this seems to allow the Fedora installer to shrink the volume, too. If you weren't able to shrink the Windows volume down enough, you should be able to shrink it further here.
On my 256 GB hard drive, Windows' Disk Management allowed me to shrink the Windows volume down to 125 GB. Afterwards, the Fedora installer allowed me to take it down to as low as 25 GB if I wanted to. I decided on leaving Windows with 80 GB.
After I booted into Windows again, it performed a disk check and then everything was fine. Funnily enough, at this point Windows' Disk Management also allowed me to shrink the volume down to 25 GB if I wanted to.