Dave
Where are you doing the NAT ie. on the ASA or the router ?
If it is the ASA then do you have two public blocks ie. one for the ASA to router and one for the router to ISP connection ?
Does the 3750 do the routing for your internal vlans ie. is the default gateway(s) of clients the 3750 or the ASA.
The 3750 connection to the ASA, is it a routed port on the 3750 or is it using a vlan interface (SVI).
Note that last question does not apply if the clients default gateway is the ASA.
Jon