Lead developer about Project X:

“Focus on responsiveness. That will probably take you the rest of the week”

The next day:

“Focus on functionality Y”

MAKE UP THAT MIND FFS?!

I feel your pain mate!

In this case (which is a very, very, common case) I always tell the other one which important things will be put aside if I do the new work right now. And then he can decide which is more important.

I don't care if I do job A or job B first, but I'm not the one who is responsible for the consequences, like missed deadlines, if priorities change faster than my underpants.