I don't know if my (or another) answer will meet your need, but I will try. I fear, sometimes, that the effort to reduce the "issues" to a bare minimum of questions masks the thoroughgoing nature of this debate. There are background commitments, a prioris, and previously studied conclusions that form a complex web of belief in which baptism is situated.
1. Are the UNBAPTIZED children of believing parents, in some legitimate sense, breakers of a covenant, and if so, which one(s)?
If it is possible in this NT age for anyone to be properly identified as a "covenant breaker," then the warnings against faithlessness under the Old Covenant (OC) are comparable to the same conditions in this present (new) covenant-era. This is certainly a key issue in the standing debate over baptism and covenant-inclusion. In a strict sense, Baptists deny that there are "covenant-breakers" today, because of the way they read Jer.31:31ff. This stance characterizes the matter of re-baptism, or as most prefer to see it: proper baptism coming after one or more false-baptisms, hence no-baptism. Since those "baptized" were unbelievers, they weren't baptized, even if wetted/dunked. The New Covenant can't be "broken"
in any sense, according to traditional Baptist thinking.
Historic Covenant Theology (CT) does not agree with the Baptist interpretation of Jer.31, when it insists that
in no sense can there be any covenant-breaking in this NC era. The distinction we insist on is that of an internal and an external connection; a substance and an administration distinction. Furthermore, we believe that the basic covenant-relationship between God and his people in OT times was substantively identical to that which obtains in the NT. Only a spiritual connection made the external connection worth anything, as much then as now; and a purely superficial connection was (and is) a double-damnation.
If baptism and circumcision are of the same
nature, i.e. essentially spiritual, and emblems of the covenant of grace; then the warning of Gen.17:14, "...he has broken my covenant," (and see Ex.4:24-26), is comparably transferred. All the other instances of faithless covenant-breaking (usually by adults, see Lev.26:15) have appropriate NC analogies; see esp. the warning passages in Hebrews. What does it mean to be a disciple? Apostasy is giving up that identity, the faith once claimed.
So yes, the Reformed have argued that it would be sinful to neglect the baptism of one's children, since it would be both refusal of a particular duty of believing parents; as well as formally rejecting visible, covenant-claims from heaven, through the church, upon an otherwise appropriate individual. Those children are
passive covenant-breakers. It is a breach of the New Covenant.
2. Are the BAPTIZED children of believing parents, in some legitimate sense, keepers of a covenant, and if so, which one(s)?
By parity of reasoning, these children are passive covenant-keepers, insofar as they are legitimately marked as God's property. Of course, there's more to discipleship than mere identification. According to Mt.28:19-20, baptism and
teaching (inculcation of the Faith) are coeval aspects of discipleship. So, those same baptized children have not only the instant privilege of indoctrination, but the duty to absorb it and make it theirs by willful acknowledgement in due season. By degrees, they (just as also an adult) lose a portion of their passive/receptive covenant-keeping into active keeping.
3. Finally, are the infant children of believing Presbyterian parents in the same status of the children of believing Baptist parents until the child is baptized – for those few days it takes to get them to church?
This question would not appear to proceed from the perspective I have proposed above, in light of the overall framework of discipleship. The matter of OT infant-circumcision should provide a helpful analogy. Was the OT child, from day1 to day8 (the prescribed day for his ritual) regarded as a "covenant-breaker"? It would seem not only uncharacteristically rigid and hostile; but how could his
failure to be circumcised be recognizable as a literal
breach of a covenant, if he were not
already by birth a particular member and party to it?
The real issue, then, is whether even in advance of such an infant-baptism the church and parents recognize that this child is a covenant-member and disciple-material by virtue of a providential birth. Is he (or she, under NT enlargement) entitled to baptism? If so, then to withhold it needlessly makes him or her a passive covenant-breaker. If it be answered, "It's not as if we will neglect to teach him, even without a formal admission to discipleship," we recognize a fundamental distinction in how children of believers are viewed, indicating different doctrines at work. Are they indistinguishable from all the rest of the children in the world?
Is discipleship initiation, in each and every case, something like an enlistment oath, a willful joining of one to the service? Or is discipleship more akin to belonging to a particular people, a kingdom? To bring the first analogy in line, are heavenly citizens only made by a
naturalization process and a personal oath of allegiance; and never by an embrace of one's providential blessedness, and ownership of an oath once taken on his behalf? Presbyterians adhere to the latter, and according to their Confession should believe their children "are in that respect within the covenant, and to be baptized," WLC 166.
Hope this is helpful.
