storage tips for fresh corn tortillas
My personal experience is that corn tortillas will stay more pliable if stored at room temperature, but may not last as long.  I'd assumed that I could find some head-to-head tests from one of the usual sources, but surprisingly not, which means that it's more likely that storing them in the fridge vs. counter doesn't actually make any difference.

Regardless of where they're stored, though, corn tortillas will only be pliable for a few days.  Even my homemade tortillas are really only good for 3-4 days, before they're good for nothing but making chips.

If you're buying them warm, first you want to store them in the open or wrapped in cloth while they're cooling (so that moisture evaporates and they don't get moldy), and then immediately put them in airtight packaging (so that they don't dry any further).

Incidentally, there's one other way of heading tortillas: putting them in a moist container (a cloth wrapper or a plastic food cointainer) and microwaving them for a short time.  This effectively steams them, and the tortillas will be pliable until they cool.