I have a default route 0.0.0.0 but I'd like some packets that come in on certain interfaces to have a different default route.
If you only wanted 192.168.1.0/24 to use the specific default route on a particular interface, something like this should work.
ip policy route-map mymap
access-list 10 permit ip 192.168.1.0 0.0.0.255
route-map mymap permit 20
match ip address 10
set ip default next-hop
Wow, this seems to be a popular answer.