I think the first thing you should do is look at why this is a counter to your argument. Your argument is in the form of "I think we should expend energy in this way." Their argument is "Why expend energy at all?" The reason this counters your argument is that it's a valid question. If you seek their help in accomplishing a goal, you should at least be able to argue that what you are going after is "better than nothing."
I would not treat this as a counter to your argument. I'd treat this as an opportunity to sell them on the value of your idea. They've set their bar at "convince me that your idea is better than no idea at all." Merely proving this will bring them back to the table.
You ask for a general solution to this one, and there isn't one. You will never find one universal solution to this which magically brings the discussion back to where you want it to be. Discussions are not one sided. You need to tailor your argument to the individual. What are their goals? Their aspirations? Why is it worth it to them to spend the energy to discuss the topic, much less actually act on any results that come from that discussion?
You will need to connect with them at this level. If you cannot connect with them at this level, it is unlikely that you will be able to connect with them at a higher level later on in the discussion. If it's your boss using this argument, understand what tasks are on his plate. Nothing sells a boss faster than convincing him or her that you can do their job for them. If its your significant other, an argument like this likely points to them being tired of you forming arguments about what improvements need to be made. If its a parental figure, they may be testing you, to see what you do next.
If it's the President of the United States that you're talking to, you might take his position literally -- POTUS's time is worth quite a lot. Your topic may actually not be worth their discussion time. You may want to go find a lower cabinet member to talk with first.
In all of these cases, the correct way to resolve this challenge is founded in your relationship with the individual. Start there first.