He demands that we shall say Christ was only the elects’ substitute, and bore the guilt only of the elects sins.  We reply, show us the place where either the Bible or the Confession of Faith says so.  the truth is, that under the question of the extent of the atonement, two inquiries come in, one as to its nature, the other as to God’s design in it.
And all intelligent Calvinists are accustomed to teach that the limitation which attaches to the atonement is not in its nature, but only in its design; while their enemies, Arminians and Pelagian, industriously charge upon them what they as industriously repudiate, that they teach it is limited by its nature. Thus Dr. Hodge “They are merely beating the air. Those who deny that Christ died for Judas as much as for Paul, for the non-elect as much as for the elect, and who maintain that he died strictly and properly only for his own people, do not hold that there is any limitation in the nature of the atonement. They teach as fully as any men, that an atonement sufficient for one is sufficient for all.” Again, he says, that “the atonement as it its nature is infinite, and as to its nature, to all, as to one.” Hence it follows, that an accurate writer, when speaking specifically of the nature of the atonement, as the committees were speaking in the first part of the third section, will properly use general terms. So does the Bible: “Him who knew no sin, to be a sin for us.” 2 Cor. 5:21, ‘He bore the sin of many,” Isaiah 53:12. “His own self bore our sins,” 1st Peter 2:24. “A ransom for many,” Matthew 20:28. “By the righteousness of one the free gift come upon all men unto justification of life,” Romans 5:18. The propriety of such language, when speaking of the nature of the atonement is so great, that the reviewer himself adopts it, as is justly stated by Dr. Waddell.  But he objects the former, while his own language is afterwards qualified by what follows, the language of the committee is not, and is thus left to suggest rather and indefinite and heretical belief, than a true one, as to the persons form whom the atonement was made. We reply that the assertion is incorrect: we do qualify.. For, when we pass, at the end of the section, from the nature to the design of the atonement, we state that the limitation, in terms fairly equivalent to those of the Confession, and fairly expressive of the revealed facts. We there teach that the design of the atonement, which is nothing else than the decree of God, limits it to the effectually called.  Southern Presbyterian [Columbia, S.C.] New Series 2, no., 4 (1863) [no page numbers].
From David Ponter's site: CalvinandCalvinism.