Well, I've successfully used that strategy to deal with hard external deadlines.
You can't just say "no, can't do it", because in all honesty, you don't know. What you can say is "based on our current estimates and priorities, it will not be possible." If they insist it is needed then they need to increase it's priority until it fits within the amount of estated work that can be done before X dates.
I think the underlying problem you are facing is viewing a set of tasks as a schedule to be set rather than a prioritized list of tasks with estimated completion dates.
You can't just say "no, can't do it", because in all honesty, you don't know. What you can say is "based on our current estimates and priorities, it will not be possible." If they insist it is needed then they need to increase it's priority until it fits within the amount of estated work that can be done before X dates.
I think the underlying problem you are facing is viewing a set of tasks as a schedule to be set rather than a prioritized list of tasks with estimated completion dates.