Generally speaking the 1gb is not going to cause any issues on a single 1920x1080 (or 1200) monitor, and less so on lower resolution. Also with a single 560 Ti, your GPU power will probably be a limiting factor much before the VRAM.
As perfectblue said, very large resolutions can eat up a lot more VRAM. They also require a lot more GPU power, but that VRAM can make a much more noticeable difference.
I would say the 2GB card is alright for being more "future proof" but it's not really necessary.