Modded Skyrim you say? Yeah, 2GB is probably not gonna cut it if you have multiple texture packs installed + Vurts Skyrim Flora Overhaul, which eats VRAM for breakfast. Just be careful with how many texture packs you use and you shouldn't have to much problems, because even at 720p the texture packs will eat up VRAM insanely quickly. The high res DLC will run fine though. I'm not sure if you play any of the Fallout games, but if you do, go nuts with texture packs as that game rarely ever uses over 2GB's of VRAM even with all the big texture packs I could find on the Nexus. The only time it does is if there are a lot of NPC's crowded into one area, but even then it only uses around 22-2300 MBs of VRAM.
Source? I have a 2GB GTX 770 that I used until my 970 arrived, and I originally thought that I didn't have to many texture packs and that my GPU was fine with the ones I was using, but nope, as soon as I put in the 970 and fired up Skyrim, VRAM usage went straight up to 2900MBs as soon as I loaded my save and went over 3500MBs after walking around for a bit. I was getting random crashes in Skyrim while using my 770 and they went away completely after getting the 970, so I can only assume that my VRAM was bottlenecking me quite severely in Skyrim.
Once again, just be careful with how many high res texture packs you mod into your game, if you don't use to many you shouldn't have the issues I had. My problem is I'm a hardcore nerd and I enjoy seeing how far I can push Bethesda's games with mods, my Skyrim looks absolutely insane now that I've optimized my mod load order for my 970. With all my mods and ENB configured for maximum quality, even my 970 drops into low 40's-high 30's in FPS.
My Fallout:New Vegas install looks about as good, if not a bit better, than vanilla Skyrim running at max graphical settings, which is insane considering the Fallout games are downright hideous without any mods to improve the graphics.
The answer to the question in your poll is tricky. If you don't mind turning down texture quality in some games then yes 2GB is enough for 1080p gaming. But if you're like me and get disgusted at the thought of turning down *any* graphics settings, then no 2GB isn't enough for modern games. It also depends on how much you like to mod your Bethesda games (Who doesn't love Bethesda games? <3), Skyrim and Fallout were pretty much my main reasons for getting a 4GB 970, considering my 770 was easily able to max out any game I played.