On the Confessing Baptist Podcast #91 dated June 16, 2015, Brandon Adams & Pascal Denault discussed 1689 Federalism (Confessional Baptist Covenant Theology) and how it differs from Presbyterian Covenant Theology. Here are some of my notes from their interaction (I changed the order of the material presented to make the thoughts flow better in writing). If my notes do not reflect the podcasters' beliefs, then it is from my misunderstanding of their discussion.
The Presbyterian view of the Mosaic Covenant is that this covenant does not have a works principle; it is the Covenant of Grace. People were saved through faith alone in Christ alone through the Mosaic Covenant, which revealed aspects of the original Covenant of Works. Under Presbyterian Covenant Theology, Lev. 18:5 is a Spirit-wrought sanctification and the fruit of faith. It is obedience that flows from faith rather than referring to a works principle (an earning or meriting that is opposed to faith). Therefore, Lev. 18:5 is a statement of the Moral Law (an abstraction); it shows a perfect rule of righteousness and not a covenant of works.
The 1689 Federalism view of the Mosaic Covenant is that it was a covenant of works (but not THE Covenant of Works given to Adam) for life in the land. It revealed information about the Covenant of Grace; therefore, people were saved by understanding the revelation of the Gospel represented in the covenant. They were not saved by the Mosaic Covenant, but by virtue of the New Covenant. Anyone who is ever saved is saved by the New Covenant. In Rom. 10:4-8, the Apostle Paul quotes Lev. 18:5 in contrast to a faith principle.
After the Fall, it is impossible to obtain life by the Law (this is plain in Paul's teaching). The Mosaic Covenant was conditional and breakable; it was Spirit-wrought obedience and not faith alone. Therefore, it cannot be the Covenant of Grace. The Mosaic Law sets forth a works principle, but the reward offered was not eternal life, only life in the land of Canaan. In Deut. 30:1-14 we have the prophecy of the future New Covenant, a revelation of the grace that is to come (see v.6 and Ezek. 11:19, 36:26).
In Lev. 18:5 the Mosaic Covenant did not offer eternal life to the Israelites, but it is a repetition of the Covenant of Works. The Mosaic Covenant does not reestablish the Covenant of Works with the reward of eternal life, but when the Israelites hear this phrase, given in a new context and for a different reward, they are reminded of what was true under Adam--that is, the possibility of eternal life for perfect obedience that was offered to Adam.
The Mosaic Covenant is not an administration of the Covenant of Grace (which is the Presbyterian Covenantal view), but it is related to it by showing us what Christ was to accomplish in order that we could have all the benefits of the Covenant and obtain eternal life. It teaches us about the Covenant of Grace by showing the Israelites their sinfulness and the foreshadowing of Christ's death upon the cross through the sacrificial system. It talked about Christ and the Covenant of Grace, but it was NOT the Covenant of Grace.
Under 1689 Federalism, the Moral Law says "do this" (a command). When a works principle is added to the Moral Law, then it becomes a covenant of works (i.e. "do this and live"). The 1689 London Baptist Confession of Faith 7.1 shows that all reasonable creatures (image bearers) owe obedience according to the law which says "do this". But God adds the reward of eternal life to the law, and thus, He gave Adam the law as a Covenant of Works which says "do this and live". This is the distinction between law proper and law as a covenant of works.
The Decalogue (or Ten Commandments) is the Moral Law (commands to "do this"). Lev. 18:5 is not just a command, but an expansion of the command "do" and the reward "live" (it is a proposition). When a reward is added to the law, it becomes a covenant of works. This is why the Mosaic Covenant is not the Covenant of Grace.
"Ye shall therefore keep my statutes, and my judgments: which if a man do, he shall live in them: I am the LORD," (Lev. 18:5).
"For Christ is the end of the law for righteousness to every one that believeth. For Moses describeth the righteousness which is of the law, That the man which doeth those things shall live by them. But the righteousness which is of faith speaketh on this wise, Say not in thine heart, Who shall ascend into heaven? (that is, to bring Christ down from above:) Or, Who shall descend into the deep? (that is, to bring up Christ again from the dead.) But what saith it? The word is nigh thee, even in thy mouth, and in thy heart: that is, the word of faith, which we preach," (Rom. 10:4-8).