Well I currently run a Nvidia 310 512 MB and yes it's possible to 720p but with very low FPS and a much lag. Also you need to post other specs of your PC too so we can help better. For now I would suggest you buy a new card. If you need any help on that come back and tell us your PC specs and budget.
1GB is enough for 1080p so 512Mb should be enough for 720p
Here the equation: 1080P = 1920X1080 = 2073600 pixels = 1024MB
720 = 1280X720 = 921600 pixels = 455MB (if compared to 1080p = !024MB) = less than the half = OK so the limiting factor is the GPU power...