Two double pole 60s usually means 120a/240v but that will be at 80% so you are looking at more like 100a. That still looks like a whole lot of toaster wire and I would want to see the plate on your air handler, maybe on the heater elements themselves.
Do you perhaps have a heat pump with a 60 on the condenser and a 60 on the air handler? That would be more likely. If you can bypass the toaster wire, it should run the heat pump if it will start it. Usually the condenser breaker is a lot higher than the full load current when running. That answer is on the name plate of the condenser
Full load amps vs Max breaker size.
You are really going to have to figure out what you have.
You may have 10KW of heat strips, too much for the genny and a 3.5-4 ton heat pump that your generator won't start If the heat pump is smaller than that and you can switch off the aux heat at the thermostat (or a separate breaker in the air handler), you have a chance.
If this is straight cool with heat strips, buy some space heaters and be careful.
