I've gone several years without needing to call Triple A, but I've called twice this month. Once when my car died on the freeway earlier this month (I was able to get well off to the side, and the wrecker came and towed it to the dealership, which was able to fix it in a day), and yesterday, when I went out owling (we DID see a snowy owl, too!). The owl flew as soon as we saw it, and I thought I'd do a U-turn (on a quiet road, with good visibility), but what I thought was an okay drive turned out to be not so okay, so I ended up stuck.
I have this to say: the sheriff officer was pleasant about it, and helpfully hung out with his flashing showing (helpful especially as it was getting to be late afternoon), the Triple A wrecker was pleasant and pulled us right out. And best of all, the friend I'd gone birding with was, as usual, just wonderful company, and kind about my mistake.
If you're going to drive off the road, do it as I did: at a very slow speed, not too far off, with soft stuff around, in cell phone reception, and with a good friend around.
More than one person stopped to check that we were okay and offer help, too, which I greatly appreciate. It's really helpful to feel like people have your back even if they don't know you and you're a crazy birder.