A friend gave me the hint of recutting the stem under running water to wash away the sap that would otherwise clog the plants plumbing. (I remember my grade school botany: xylem up, phloem down. Is milkweed a "vascular" plant?) Then quick plunk the stem in a vase of water.
I posted in another thread... I strip cleaned stalks and put the leaves in 1/2 gallon ziplocs. Those are stored in the crisper drawer. I keep about 6 on hand as I go through about 1 an 1/2 per day. But they are always fresh. I also find the cats to be really fond of the seed pods. THey last longer as well.
I definetly do the bottled water method when I need a lot of milkweed handy as the cats appetites increase, otherwise I remove the leaves and let them soak in water until needed. This keeps them nice and fresh.