I have a configuration file (gpsd.default) containing data with the following format:
# If you must specify a non-NMEA driver, uncomment and mod
This is because you are using a regex containing /, which is the same character sed uses as delimiter.
Just change the sed delimiter to another one, for example ~:
sed -i 's~^GPS_DEVICES="".*~GPS_DEVICES="dev/ttyUSB1"~' /etc/default/gpsd.default
By the way, since you are changing files in /etc, you may want to use -i.bak, so that the original file gets backed up. It is a good practice to prevent loss of important information.