What does one say if the controller says to turn to heading xx, you repeat the instruction and turn to heading xx and then realize that was not a good choice. What do you say to go back or get out of it. "unable to continue present heading, turning back to heading xy"?
It seems with my limited experience with ATC, they do not allow much time to think about the instruction before they expect a reply.
That would be an appropriate response, yes. Or, initiate the following conversation:
"Center, SpamCan 345 needs 20 right for weather."
"SpamCan 345, 20 right approved, proceed direct destination when able and advise."
If they come back with...
"SpamCan 345, unable."
Then you can negotiate with them.
"I could alternately do 20 left, would that work?"
If they continue to be uncooperative, you can declare an emergency, and then they have to accept whatever you ask for.
Here's an interesting story from a few years ago. Laurie and I were flying the Aztec to Cozumel, and there was a pretty nasty storm right on an airway that had active MOAs or restricted areas on either side of it (I forget which). Every airliner on that airway was asking for deviations. ATC responded:
"[airliner], unable due to active restricted airspace on both sides of the airway. But if you absolutely have to deviate, you can squawk 7700 and deviate however you wish."
He told this to probably a dozen airliners while we were talking to him, and they all chose to do it.