You in general don't want to set it to a interface because it is dependant on proxy arp to work but to your issue.
Unless a gig port works different this means that this is a switch port. IE you did not type NO SWITCHPORT on the interface. In general you have to also place a IP address on the interface since it is not much use to turn off the switch port and not have a ip address on it.
If it is a switch port becuase it is something like a trunk then you only option is to use a vlan interface as you route destination. This is also a bad idea since you now have arps possible going out many interfaces.
Best bet is to find a IP address can act as your default route.
