What is called "the impossible gospel" is also called "the celestial law" by other anti-Mormons. This was a favorite of our old friend Coleen Ralson (of the infamous Nauvoo Christian Visitor Center) who had a display set up about it at the NCVC.
The way it works is that the anti-Mormon quotes a few scripture that talk about the need for complete obedience or complete repentence. The scriptures include
They also use a few quotes from general authorities that talk about the need to repent of all sins and to be completely obedient.
Once they can convince the Mormon that he or she must be completely obedient and never repeat past sins in order to qualify for grace and salvation (and they use 1 Nephi 3:7 to show that God wouldn't ask this of people if it were not possible), then they back the Mormon into a corner where the Mormon "must" admit that he/she is not forgiven or saved and never will be under the Mormon "celestial law" (or "impossible Gospel").
So here is a way to respond to a Church member who has been subjected to this line of reasoning.
It can be pointed out that this issue of extracting doctrine from scripture alone and then arguing over whose interpretation is the best is EXACTLY the sort of thing that led to the Great Apostacy, the Protestant Reformation, and the utter disintegration of Protestant unity. The very process that the anti-Mormon is using (private interpretation of scripture in opposition to the teachings of living prophet and apostles) is wholly rejected by the Latter-day Saints as an apostate and contra-biblical exercise of human will in rebellion against God.
The anti-Mormon will try to press the Latter-day Saint to then exegete those passages in a way that doesn't contradict LDS doctrine. The member has a few choices.
The only thing left from the LDS apologetic side is to provide our LDS friends with some possible interpretations of those proof texts used by the anti-Mormon.
The anti-Mormons will say "this is Mormon doctrine" as they then assemble their proof texts into an argument.
But the member should become immediately suspicious because (1) he/she has never heard that taught before and (2) the anti-Mormon is trying to convince the Mormon "what the Church REALLY teaches and believes." The instant you have someone working hard to convince you that the Church "really" believes something that you have never heard of, you can be pretty certain that you have a certifiable anti-Mormon on your hands. This is a classic tactic.
And all this stems from their worldview that doctrine can ONLY be extracted from authoritative texts through careful exegesis and paying close attention to the details of individual words within a verse. They simply don't have room in their belief system to allow for inspired, true teaching that "misuses" scripture (i.e., that uses unusual, counterintutitive, or questionable readings and interpretations of scriptures). This is despite the fact that New Testament writers engaged in the same kind of "scriptural abuse" (e.g., Matthew 2:15 --- "Out of Egypt have I called my son."). The idea that authorized priesthood leaders can teach truth outside of, or in apparent contradiction to, scripture is simply anathema to them.