I've often received comments to the effect of "you think X is Nestorian, so what?" or "what is the big deal about Cyrillene Christology?" After removing my jaw from the floor, I realize that there are actually people out there who don't comprehend the problem with Nestorianism. Well, it's very simple: if the one who died on the Cross was not divine, then we aren't saved. No matter what your theory of salvation, whether it's incarnational, sacrificial, penal, or all of the above, it all hinges on the person on the Cross being divine. But the only way that can be the case is if there is a natural union, a hypostatic union. Union by grace and love, as Theodore of Cyr and Nestorius himself advocated, happened all the time in the Old Testament, but those people didn't and couldn't become divine in the sense of actually being God, no matter how profound the degree of love or grace expressed. That's why St. Cyril was so tenacious against Nestorius; Cyril believed that Nestorius was denying single-subject Christology because he refused to affirm the necessary hypostatic/natural union.
So the simple answer is: if Nestorianism is true, then there is no Gospel. The so-called "good news" of Nestorianism is that Christ does not save us, which is actually the worst news we could possibly receive.
UPDATE -- Thank goodness for Wayne Grudem. His discussion in Systematic Theology (2000), pp. 552-563, covers the issue from an Evangelical perspective without blowing it on the subject of person. I still think he goofs by relying on Brown's account of Nestorius on p. 555, but at least he doesn't commit the same errors on personhood.