Sure you can. The trouble is, for people who don't have a habit of exercising, not having a fixed plan makes it very easy to decide not to do anything at all. In fact it's quite easy to make that decision even if you do exercise regularly!
There'll be lots of tips around for how to incorporate a bit more running into your normal routine. My advice would be firstly to realise that run/walk is the paleo approach to avoiding zombies and will be a lot easier than thinking you have to 'run' for 5k straight. Training wise it'd be all about running as fast as you can until you start to slow down, walking as long as necessary to recover, then running fast again. It's more enjoyable, you can make a game out of it like running between lamp posts or to a specific tree behind which you can hide, and less demanding on the joints etc as they also get recovery time. Practise that and you'll be able to deal appropriately with zombie-inspired hysteria. Who knows, by May you might not bother walking much at all.
This requires some effort of course. How much depends on how much time you have available. If you can find a half hour twice a week (to include some warm-up walking, 10-15 minutes of variable speed running and some stretching to make life easier) then I don't think you'd need more than that. To deal with the lack of regimentation, I'd put something up on the wall that was clearly visible every day, maybe with stickers or something for your allotted total number of session (say, 25) and you get to put one in the zombie column every time you complete it. This doesn't force you to working out on any particular time or day, or even necessarily to the twice a week thing, but it does mean that if you fall behind on the commitment you make now you'll have a visual reminder of the workouts you still have to fit in before the deadline. I don't know if I've explained that very well but basically bargain with yourself that you are going to let yourself choose if and when to workout but you have to do it (at least) a specific number of times before the apocalypse. And use pretty colors.