I had a very similar problem yesterday on my way back from Indian Wells. I stopped by Tejon Ranch and hit a pothole on Laval Rd (you'll see it if you're coming from the south). An hour later, as I was leaving, I got the "very low tire pressure, pull over" warning. Lo and behold, there was a crack in the sidewall and I could hear the leak. Not ideal when it's past 9pm and you're in the middle of nowhere, 300 miles away from home. So I took out my $40
Slime Flat Tire Repair Kit and temporarily "fixed" the tire. The safe thing to do would have been to drive to Bakersfield 30 miles away and go to a tire shop in the morning but I didn't feel like it so I just kept driving, recharging at Harris Ranch and then Gilroy. I had to re-inflate the tire twice along the way but it held until I got home at 3am. I called Tirerack this morning and they're shipping me a replacement tire at 50% off.