As kelthic said, for that resolution it would be fine. If you plan to use Nvidia Surround or Eyefinity, then yes, VRAM will be the issue. But at 1680x1050 1GB will be more than enough. Coming from experience as my brother has a monitor with that resolution, and using a 560Ti.
I run the same resolution with an ASUS GTX 570 and its brilliant. The 570 is a much better card than the 480 as it runs quiter, faster, cooler as it was pretty much designed to replace the 480. New and better tech means it will last you for quite sometime and thats before you even OC it.
1680x1050 pretty much means you can ultra every game out there with a 570 and it will do a good job at higher resolutions.
If you are looking to move up to a better resolution at some point though then its probably best you go for a 580/680 if you want the maximum out of your games.
LOL point is that cards are always cheapest at launch then they go up a bit and now they are closer to the same price as when they launched and noobs think they are getting a deal when they are just paying finally the MSPR that they should have been paying all along.