As long as that line isn't clogged, the water will darin through it into a drain and not overflow onto the floor.
Do you have good cold water pressure? Check the supply valve on the hot water heater. It may be partially closed. If the cold water pressure is also sporadic, check the shut-off valve for the entire house. It may not be opened all the way.
Also check the bypass valve on the softener to make sure it is open.
Empty as much water out of the softener as you can. Use a pail or large mug. Now watch the water level for a few days. Also note whether the softener recycles and thw water level after it cycles.
Post again in a few days to let us know what is happening.