$250k per account, up to 6 accounts. So the FDIC insures up to $1.5 million. If you have more then that, I think you can find other ways to secure your money.
Anything above FDIC insurance limits and you’re in US Treasuries, backed by the full faith and credit of the US Treasury. They’re one of the safest financial assets in the world. The risk of default is almost, but not quite, zero.
The FDIC could not make the system solvent in the event everyone tried to redeem their funds. It can only keep up confidence to try to prevent people from all trying to redeem their funds.