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Baptistic covenant theology would say that, although Christ is the Savior of all the OT saints, He did not die for all in the Old Covenant. Based on Jeremiah 31/Hebrews 8, Christ died for all in the New Covenant. Hence, this is why it is called a better covenant built on better promises.
Christ died (1) in a general way for all--common grace, and (2) He died specifically and effectually for the elect in both the Old and New Covenant. The problem is not "For whom did Christ die?," but how do you know for "Whom Christ specially died?" (i.e. who are the elect?). We don't know and thus baptism is not based upon this "actual knowledge!" For adults it is based primarily on a profession of faith and for children--the household baptism is more in line with the O.C. We must remember that the New Covenant is after the pattern of the Old Covenant (Heb 8:5, etc.). Thus, the New Covenant is a fulfilling and not an abrogation of the Old Covenant.

Now we must ask ourselves, “How the N.C. is fulfilled in the O.C.?” First, circumcision though no longer needed in the N.C. , had to be fulfilled some way? (it no longer is necessary in the N.C. relationship, but God’s law is holy, just, and good, and it can’t be abrogated, so it must be fulfilled). Second, it was not fulfilled by Christ being circumcised/baptized for all believers—for there is still a command for adults and infants (household baptisms) to be baptized. Thus, a sign still remains in the N.C., as in the O.C. (i.e. circumcision/baptism). So, what is the solution?

The solution is clearly seen in Acts 2:39 saying, “For the promise is for you and your children and for all who are far off, as many as the Lord our God will call to Himself.” Words are not here or elsewhere in Scripture by accident. What is being used here is O.C. language. What is in view here is not a profession of faith, but God’s effectual calling which will lead to a profession of faith in elect adults. However, the promise is not only to those who are effectually called and thus respond everywhere (Rev 5:9). The phrase and your children is added as well (these can’t respond by profession as with children not being able to respond in the O.C. with circumcision). The text clearly states that called children of covenant believer’s have a covenant promise (this does not mean they are or necessarily will be saved. In the O.C. community there were lost and saved members and thus in the N.C. as well)! What is the sign of their promise if not baptism? This naturally and hermenutically leads us back to the Abrahamic covenant and in finality to the truth of paedo-baptism.

Reformed and Always Reforming,