On your specific Honda mower, there is a constant-tension belt that runs between the engine and a pulley on top of the transmission. When you turn the SmartDrive control, it pulls a cable that gradually engages a clutch inside the transmission, increasing the power to the rear wheels.
So the belt may have slipped off, (unlikely it actually broke), the cable may have come loose at either end (or just way out of adjustment) and lastly, there may be an internal fault in the transmission itself. All of these are generally covered under the 3-year warranty, but it is a very busy time for a lot of lawn & garden dealers. You may wish to call around and maybe find another Honda dealer who could look at it sooner.
If you'd prefer to DIY, I can post a few pages from the Shop Manual that show some troubleshooting and repair diagrams...let me know.