I guess Yes.
do the following on 3750 L3 .
Create Vlan's for 10.10.10.1 /16 and 128.128.128.1/24 on 3750.
Add the default route poinging towards 10.10.10.1 on 3750 switch.
iproute 0.0.0.0 0.0.0.0 10.10.10.1
assuming 2960 is free from vlan's means you are not configuring anything on 2960 switch.
Thanks,
satish