The main problem is that the grid-tie inverter expects to deliver all available power from your solar panels to a load - either your home and/or the grid. Aside from being picky about a clean, 60 Hz sine wave, I would expect the inverter to shut down if its output voltage dropped too low (short circuit - grid power outage) or went too high (main breaker open). So without the grid connected, the load would have to be managed carefully to keep the inverter on.
One way to manage load would be to charge batteries, as explained by Eric Friend above, but the batteries would be costly, defeating the point of trying to get value out of your existing expensive system. Trying to balance household load with available solar power would be complicated. But depending on how picky the inverter is, perhaps an inexpensive load, such as resistive heating, could be set up to automatically dissipate unused power.
So for example, if your solar panels are delivering 4kW and you have a clean sine-wave inverter providing 200W from a motorcycle battery (cheap because it is only 200W), and a household load of 2kW, then you could switch on, say, eleven 200W heaters using automated relays to dissipate the remaining 2.2kW of power.
To start such a system, you would turn off the main breaker and turn off all loads to your house except for one 200W load. Then you would turn on the 200W inverter to make it appear that the grid power has been restored to the grid-tie inverter. When the grid-tie inverter turns on, enough (i.e., 4kW) resistive load would have to be immediately connected quickly enough to keep the voltage stable. Then household loads could be connected, provided that equal amounts of resistive load automatically disconnect quickly enough to compensate.
Please correct me if I'm wrong, but I don't think this system would be likely to shock any linemen because, if the main breaker were to be closed, then the entire neighborhood would be loading the circuit, causing the voltage to fall below nominal and shutting the inverted off by its own anti-islanding protection. The 200W inverter would also hopefully shut off when shorted rather than self-destructing. If this is still a concern, it should be much more relevant to the backup generators that people are connecting to their houses in case of a power outage.