I have received a question concerning the atonement and salvation. These responses below are very specific, but they are to two main objections. First, that if one allows for a free will view of man (where man can choose to believe on Jesus Christ for salvation), then one gets to "play a role in one's own salvation." Second, that if one can choose Christ for salvation, then his exclamation of "It is finished!" on the cross is really quite premature, and cannot be said.
Most of the problems in these types of debates surround definitions of terms. There are so many, and very few (or sometimes none) of them are defined. So what often happens is they are common terms infused with meanings separate from what you or I would believe; or they are terms that take on the same meanings at first, but later change unannounced.
For instance, what does "play a role in one's salvation" mean? To the average person, this sounds like "do something to earn one's salvation" or "help God secure the payment/grace for salvation," both of which orthodox Christians everywhere would reject. But if this is what it means, it's unclear that merely choosing to accept Christ's offer of salvation *is* playing a role in one's salvation so-defined. More likely, "playing a role in one's salvation" in this context means something like "doing any action or being the primary cause in a state of affairs that functions as a necessary or sufficient cause or process to bring about salvation in one's own life." But in that case, the argument only works for those who already believe that by believing on Christ one has contributed to his own salvation (in a negative sense), and so it's flatly question-begging without the ambiguity.
As to the pastor's argument, I really don't see the problem he does. For consider the problem of the subject's existence. At the time of the cross, it was the case that some believer, you, for example, did not exist. This is orthodox; belief in the pre-existence of the soul is heterodox. This is extremely important. In order for you to actually be saved, you must exist (a saved but non-existent individual is logically incoherent as non-existent things do not have properties in an ontological sense). At the time of the cross, therefore, you are not saved. So whatever solution the reformed pastor comes up with for solving this problem is available to us as well for our problem. Suppose he says, "But Christ's sacrifice is pre-causal, so that the effects of the cross carry out into the future, so there's no problem." But then there is no problem for us as well. For simply because certain conditions have not yet obtained (your existence for the pastor, and your belief for the Arminian), it does not follow Christ cannot say, truthfully, "it is finished." Thus, the pastor is forced either to drop the objection or to be heterodox in his belief concerning the existence of the soul.
"Reconciliation" is another term rife with ambiguity. It's important to note that biblical terms are not always univocal; they often have different meanings depending on the context. "Love" and "salvation" are two classic examples. To answer your question about the cross adequately would take an entire volume. To answer it succinctly: at the cross, the payment for sins was made. Jesus Christ bore the wrath of God so that the ontological basis for salvation would be taken care of. That basis of salvation is often referred to as the reconciliation of God to man (note that Paul says God was "reconciling the world to himself," and there's no hint of it being a restricted group). However, this is not the same as the appropriation of salvation; salvation applied.
Consider the paradigmatic Old Testament example. Moses and the Hebrews were to kill a lamb and spread its blood over the door and on the sides (almost forming a cross, cool huh?). When the angel of death came, if he saw the blood painted across and on the sides of the door, the household (family) was spared. If he did not see the blood, the firstborn would die (no matter how old or young). The sacrificing of the lamb was a necessary condition; "without shedding of blood there is no remission of sins". Without the application of the blood, one would still be under punishment.
So it is with Christ's sacrifice. His death was a necessary condition for the imputation of righteousness and justification (legal salvation). But the imputation of righteousness only happens when the blood is applied (faith in God--cf. Romans 4), otherwise, the person is still under condemnation. What happened on the cross was the sacrifice to God the Father of God the Son. That beautiful picture is why Jesus could say "it is finished." What is finished? The full-process of salvation for every individual? No. That's nowhere to be found in context. Instead, what was finished was the greatest love known to man--the payment for our sins.