I recently had this problem on a CO MR. After the CO flights were cancelled I got rebooked on UA, then those were cancelled so I just asked for a refund. No problem, and not worth the hassle given the weather. It was annoying though since it was my best one yet (2.4 cpm).

As for how long out you can go when rebooking, my only experience has been due to mechanical issues. Since you're already at the gate, sometimes they can be nicer in person. In one case I showed up at 6 AM to find the plane was delayed until 10 AM due to mechanical. There was no one at the gate, but the GAs talking to each other mentioned screaming passengers at check in. In comparison, I was easy.

I admitted I was doing a MR, didn't care if I had to go home that day, and asked if I could think about my options. Came back 10 min later telling them I was busy until May, and they said that was fine and rebooked me anyway, with a better itinerary and in B instead of L. I still got my meal voucher, too.