Here is A.A. Hodge stating dual damnable heterodoxies of salvation conditioned on faith (instead of on Jesus Christ ALONE), and that there is a sense in which Jesus Christ died for everyone without exception:
"VII. This Priesthood of Christ is absolutely perfect.
1st. He has been the medium of communication between God and man from the beginning, through all stages of human history...Through his atonement not only all adult believers, but all dying in infancy, all idiots, and all who have been saved by any extraordinary means known only to God, are reconciled to God and stand absolved from guilt.
2nd. He is, in the complete and permanent and saving sense, the Priest only of his own people, his sheep, those from the beginning given him by the Father, those who believe on him through the effectual call of his Spirit. Nevertheless, it is true that in a very important sense he has always been the Priest of the whole historic human race. He is the second Adam. He took upon himself human nature, the seed of Abraham. He was made under the law, and fulfilled the obligations, preceptive and punitive, which rest upon all men alike. He arrested, in behalf of the whole race as a body, the immediate execution of the legal penalty. The whole course of human history, of all peoples and nations, of all religions and civilizations, has been evolved under the shield of his cross, under a dispensation of arrested judgment or forbearance secured through his mediation. He, by his expiation, removed utterly out of the way of all men alike the objective hindrances in the justice of God and in the judgment of the law which rendered their salvation absolutely impossible. In this general sense, Christ, as the man whom God has appointed Priest, is the common bond of the whole human race, and his meritorious service the common basis of all human history.
3rd. But while he, in his priestly work, has made the salvation of all men possible on the condition of their accepting it, he has made the salvation of those whom the Father has given him certain by purchasing for them that faith which is the condition of their personal participation in his work" (A.A. Hodge, Evangelical Theology, pp. 218-219; underlining mine--CD).
[cf. Jonathan Edwards on Christ's mediatorial work]
