If you wanted 0.66 units and got 66 units, I am pretty sure you would die. I would count on the tissue around the infusion site not having enough throughput to release it all into your system at once and swelling up. This would mean the problem would spread over a few hours, but it would be an extreme emergency anyway.

To put it into perspective (at least with my insulin to carb ratio, it varies from person to person), if you wanted to drink a regular sized can of coke, you would dose 3.3u. 66u is therefore enough insulin for 20 cans of coke.

Another way to put it is that 10g of sugar ~ 1u of insulin. You'd have to eat 660g of raw sugar.

There is a medication called Glucagen which is used to treat severe hypo. It works by triggering release of stored glucose from the liver. The thing is, from what I've quickly googled, a typical 1mg dose is usually only enough to raise your blood sugar by about 100mg/dl, and then your store is depleted and further doses have no effect. With my insulin/carb ratio, I would only need about 2.5u to reduce my blood sugar by 100mg/dl.

All of a sudden it feels scary to think that the reservoir in my pump holds about 300u of insulin...

It will drop the blood sugar level dangerously low and cause hypoglycemia. A person can lose consciousness, get into a coma, or even die.