is that impossible?
Absolutely not. But Adobe doesn't have a tool to do this task is not a professional-level tool, with the kind of functionality that a print professional would use. So of course the learning curve is really steep.
And frankly, the task you're proposing (automated update of biz card content so you change it once in one place and all of your changes propogate elsewhere) can be automated in Word. There's no reason, in either Word or InDesign (or TBQH in Illustrator or Photoshop) to make the same change across twenty business cards manually, or to paste the same image twenty times.
It might have gotten lost in Mike's reply (he referenced many different kinds of functionality) but the one InDesign idea I'd want to point out is the idea of linking a file. Let's say you make a file like JoeBizCard.PDF in the Design Application Of Your Choice. You place it into ID, creating a link, and then copy/paste that link nineteen times. Sounds like your original workflow, right? Then Joe changes his cellphone number. You change it in your source file, and then make a new PDF. The next time you open the InDesign file, InDesign notices that the link source - your JoeBizCard.PDF - has changed, and asks you if you want to update. You do, right? You want InDesign to update all 20 links to your new PDF automagically? Instead of pasting twenty different times?
Anyhow, mind that steep learning curve. Once you clamber up, you'll find that the view from up top is splendid, and you'll forget all of the bruises and scrapes and abrasions and muscle aches you acquired as you climbed up.
If you'd rather get a how-to-automate-this in Word, go hit up the Word MVPs. I'm sure that they can help you figure out how to use one of the many ways to perfom this automation in Word. I only know, um, four, but doing anything but "writing words" in Word feels like I'm trying to drive a nail with the butt-end of a screwdriver. It's a great tool for writing stuff, but I don't use it for anything else.
