Linksys Wireless Router :: Wrt54gs - Extend Wifi / Configure Devices For Ssid

I have two WRT54GS routers. I want to extend my WiFi from the router connected to my upstream in the office to a second router in the living room. I want devices configured for the SSID and passphrase of my current WiFi (which is find in the office) to work seamlessly in the living room. I understand I can do this by running a cable and configuring router 2 as a client of router 1 with router 2 exposing the same SSID and passthrase on a different channel.
 
But I really don't want to run a cable.There is a point where a client can see router 1 where an AP would cover the living room.
 
Can I put router 2 at that point, have it connect wirelessly as a client to router 1, and have it expose as an AP using the same SSID and passphrase? Can this be done without wiring the router?