It depends upon the kind of grass. Some would regrow quite happily from the crown, over and over again. Is the garden in active production right now?

If you are opposed to herbicides, you could begin layering several layers (8 or so) newspapers over your garden area, keeping it wet as you go. Then apply a two to three inch layer of organic mulch on top of the newspapers. If and when grass and weeds emerge from this organic layer, they will be easy to pull or to sizzle.

The only thing in active production is the rhubarb at the end of the plot. So I could do the newspaper thing. If I do it now, how long do I wait before I can plant? I think it is likely lawn grass. Around here, that would probably be a fescue mix. I don't mind getting on my hands and knees and pulling weeds, but I hate pulling up grass!