If you are referring to a wireless router upstairs then I would recommend getting a range extender for the lower portion of your house. It's essentially a wireless repeater. Or, a wireless bridge with a wireless access point attached to it in the lower portion of the house. Either way you will get similar results without having to run a cable from the first wireless router.
This WOULD be the case if someone wanted to connect each router to a different broadband modem... But if you connect the routers together, and disable DHCP on one, it will work fine. It would be similar to connecting a switch to a router... it would working fine. I had a setup like this when I was at my parents house. Cause I had a few PC's in my room, and my PS2... wasn't going to throw down on wireless for all of them, and I already had a router, no need to run 3 cables when I could do 1.