Well, that depends on the game, resolution and settings you will use.
I´ve been running a GTX760 2GB since its launch and never had any issues so far. Been playing @1080p games like Dying light, GTAV, Witcher 3, The Division, etc. Not maxed out of course, but some games with High settings, another ones with Medium settings. I even play Assetto Corsa in triple screen @5760x1080 and don´t have a single stutter.
Since you asked about The Division Beta in particular OP, I´ve played with a mix of Medium/High settings and got anywhere between 35-50 fps. No stuttering.
BUT, buying a new card now or upgrading a GPU, you would want to go with a minimum of 4GB, no question. Possibly looking at 6GB.