Miller,
This subject has been brought up several times. So you might do a site-search on the topic.
The issue really comes down to "who rightly understood Calvin?" Did those who penned our Confessions get Calvin right? Or did the Amyraldians? The question comes down to understanding "purpose" as it relates to Christ's atoning work. Reformed orthodoxy settled on the "sufficient-efficient" distinction when speaking of Christ's death, one for the world, the other for the elect.
Those who disagree with this formula insist (wrongly in my opinion) that this distinction is false, because there must be an "efficiency" regarding his death for the world. And they hang contingent on this reading the honesty of the free offer of the gospel. The sins of the reprobate must, they say, actually have been atoned for in the intent of God's heart. There is some suspended transaction, then, so far as application goes--the expiatory/propitiatory benefits which actually belong in particular to individuals not being (never) applied to them due to the absence of faith.
But, of course Calvin never spoke in terms of suspended transactions either. Although the finer points in question waited until the generation following his for clear definition, the question again goes to "who can rightly claim their view as a re-expression of Calvin's thought?" Though Calvin spoke of the world-wide extent of God's mercy in Christ, the intent of it in his speech goes consistently to the elect. Calvin in at least one place expressely declares that Christ's "blood was not shed for them [the wicked]."
Both in Calvin, and later in Reformed orthodoxy, the work of salvation was seen as one grand design, terminating in Christ himself and the elect for whom he came. To create an intention beside (or even at odds with) the salvific one for the elect is to make the cross, in some cases, "of none effect." And, contrary to Jesus express declaration in John 17, it separates those for whom he died into two camps--one for which he intercedes effectually, and another for which he doesn't (esp. cf. vv. 2, 9, 19).
Simply put: if Jesus died for you, then he prays for you, and the Father always hears him (Jn. 11:42); and if he doesn't pray for you, then he didn't die for you, because "for their [those given him out of the world] sakes" he sanctified himself (17:6, 19).
I suggest reading Roger Nicole on this topic. If you can find Standing Forth (one volume of his collected writings), he has an entire section on the Atonement, dealing in part with the disputes over Calvin's view.
