I agree with Bruce. In short, the Mosaic Covenant was an administration of the Covenant of Grace; that's what it was. And yet, within this covenant, there indeed contained the CONTENT of the Covenant of Works ("Do this and live, or, Do or die"). Still, this content was not a republication of the Covenant of Works itself--it was rather a repetition of the content of the original covenant of works, made with Adam. This was and is the classical reformed and puritan view. There were puritans who disagreed with this, but in doing so, they acknowledged they were the minority.
I believe its really important for us to acknowledge both elements, there are dangers in denying either aspect. If, on the one hand, we affirm the "Do this and live" principle, but fail to see that the Mosaic Covenant belonged to the Covenant of Grace, we get ourselves in trouble. And if, on the other hand, we acknowledge that the Mosaic Covenant was part of the Covenant of Grace, but in a way that we completely deny the "Do this and live" aspect, we will be thoroughly confused and confuse others.
The Puritans often distinguished these aspects in this primary way: in their understanding of the Law as both "largely" taken and "strictly" taken. You find this in the writings of almost all the puritans that wrote more extensively on the covenants. "Largely" taken, means considering the Law as encompassing BOTH the Moral Law with its commands and threatenings; AS WELL AS the gospel as revealed in the Law, mostly through the ceremonial law--the sacrifices, etc. This is how we see the Law as a whole, and this is why the Mosaic Covenant is part of the Covenant of Grace. But, if we "abstract" the Moral Law aspect, and consider the Law as "strictly" taken, that is, abstracted and considered apart from the gospel elements revealed at Sinai, then that aspect is well considered to be a pure repetition or restatement (but not actual republication) of the Covenant of Works. So then, the Law as "strictly" taken indeed says, "Do this and live"; but the Law as "largely" taken says "believe and live."
Francis Roberts was a puritan who wrote a massive treatise on the covenants. He says: “the Law may be considered, more largely, as comprehending the whole doctrine and administration of the Sinai-covenant, as delivered by Moses on Mount Sinai; [but also] more restrictively, as it is an abstracted rule of righteousness consisting in precepts, threats and promises; holding forth life upon a condition absolutely impossible to lapsed men; viz, perfect and perpetual personal obedience to the Law; but denouncing the curse and death upon the least contrary failing. In the latter sense Paul understands the Law in Romans 10:5 and Galatians 3:12; and in this sense, the righteousness of the Law stands in perfect doing: 'the man that does them shall live in them'. . .In the former sense, which is more complexive and comprehensive, Paul understands the Law in Romans 10:4 and in Galatians 3:23-24; and the Law thus taken is a Covenant of Faith in Christ Jesus, holding out life and happiness only upon condition of believing in Christ. . .To this effect says one, 'The Law in itself considered, exacted perfection of works as the cause of life; but when that was impossible to man by reason of the infirmity of his flesh, it pleased the Lord to make known to his people by the ministry of Moses, that the Law was given, not to detain men in confidence of their own works but to lead them unto Christ'. . .For though the Law of righteousness promise a reward to the keepers thereof; yet after it has shut up all men under sin, it does substitute another righteousness in Christ, which is received by faith, not purchased by merit of works.' In both the former and latter sense, the word 'Law' seems to be used in that passage, [Romans 3:21-22]: “But now apart from the Law (IE, strictly taken) the righteousness of God has been manifested, being witnessed by the Law (IE, largely taken) and the Prophets, even the righteousness of God through faith in Jesus Christ for all those who believe”. . .[Thus] the Law largely taken, holds forth life on condition of believing in Christ, and in this notion it was given in the Sinai-covenant, which therefore is a Covenant of Faith [IE, Grace]; [but] the Law strictly taken requires perfect doing, and in that sense Moses gave it not, nor is it a Covenant of Faith but of works.” (p773-75).
Roberts goes on to sum up the Mosaic Covenant in this way (exceptional stuff):
1) “That the Sinai-covenant was purposely so dispensed as to tender life and happiness upon two opposite and contrary conditions; viz, works and faith; perfect doing, and believing: a) Upon perfect doing all in the Law: Romans 10:5; Galatians 3:12 with Leviticus 18:5; the curse being denounced against the least failing, Galatians 3:10 with Deuteronomy 27:26. b) Upon believing in Jesus Christ the Messiah promised, Romans 3:21,22 and 10:6-12; compared with Deuteronomy 30:11-14. . .To deny this, which is so clear, will but tend to weaken Paul's authority, [and] to darken many Scriptures both of Moses and Paul, and to strengthen the objection.”
2) “That, in this Sinai-covenant these opposite conditions, of perfect doing under pain of curse and death, and of believing in Christ, are very differently required and revealed. a) Believing in Christ is revealed very sparingly and obscurely; b) perfect doing very frequently and plainly. . .Whence (as Calvin notes) though the whole ministration of the Sinai-covenant belongs to Moses' office; yet that function most properly and peculiarly seems to be ascribed to him, which consisted in teaching what the true righteousness of works was, and what rewards or punishments attend upon the observers or breakers of the Law. . .”
3) “That, though these two conditions of perfect doing, and believing, be thus differently revealed and required in the Sinai-covenant; yet believing in Christ unto life and righteousness was therein chiefly and ultimately intended, and perfect doing only urged upon Israel's subordination and tendency to that believing. . .perfect doing upon pain of curse and death was urged upon Israel only in subordination and tendency to believing and the righteousness of faith, [for]. . .The Scripture, peculiarly the Law, hath hereby concluded all under sin, that the promise by faith of Jesus Christ may be given to them that believe. . .”
4) “That, the condition of perfect doing under pain of curse and death, convincing the sinner of his sin and misery, leaves him hopeless in himself. . .but the condition of believing gives him hope, without himself, in Jesus Christ, to trust to him alone for justification.”
5) “That the Sinai-covenant tendered life and happiness upon these two opposite conditions of perfect doing under penalty of curse and death; and of believing in Christ; because both these conditions were necessarily required to the sinners' happiness: [whether] in the sinner, or the sinners' Surety: a) Perfect doing of all God's Law upon pain of death was required to the sinners' happiness: because God's covenant of Works, at first made with Adam and with all his posterity in him, but broken by them, cannot be eluded or evaded. They must do it, or die; otherwise God himself should not be just and true. Do it, in their own persons, they could not, because the flesh was weak; therefore they lie under the curse and death. This covenant hereupon (such the contrivance of God's infinite wisdom and grace) reveals the sinners' Surety Jesus Christ, who alone could satisfactorily bear this curse upon himself, and perform the duty of the Law to the uttermost, for the sinners' redemption and righteousness. b) Believing in Christ is also necessary to the sinners' happiness: because without faith his Surety's perfect doing and enduring cannot become his by imputation.”
6) “That, perfect doing on pain of death, and believing in Jesus Christ are so required and conditioned in this Sinai-covenant, as to let all men see, that the penalty and duty of the Covenant of Works, have their plenary accomplishment in the Covenant of Faith [IE, Grace] through Jesus Christ alone. . .Herein they are directed unto Jesus Christ by faith, for life and righteousness. Thus according to the tenor of the Sinai-covenant, the Covenant of Works has its perfect accomplishment in Christ—by doing and enduring, all which becomes ours—by believing. Thus the Covenant of Works is digested into, incorporated with, and wholly swallowed up by the Covenant of Faith. Thus perfect doing is attained by believing.”
7) “That, the condition of perfect doing being thus attained by believing, with greatest ease unties the knots of many difficulties, and unveils the secret of many mysteries. As, a) how mercy and truth have met together, righteousness and peace have kissed each other. . . b) How sin may be condemned, and yet sinners saved. . . c) How sinners are at once justified by perfect doing, and by believing. By perfect doing, in Christ's person, to whom the Law drives them, by exacting impossibilities of them. By believing, in their own persons; whereunto the law allures them, by representing Christ as the scope and end of the Law to them. Thus it's no paradox for sinners to be justified, in the sight of God, both by works, and faith; by Christ's works, by their own faith. d) How sinners can do nothing, and yet can do all things, the Law requires. In themselves, through the weakness of the flesh, they can do nothing, as the Law requires; viz, exactly, without the least failing; and yet in Christ, the perfect Performer of the Law, embraced by faith, they can do all things perfectly; Christ's perfect obedience being imputed to them by faith. This Sinai-covenant therefore, requires perfect doing from the sinner under pain of curse, that it may drive him from himself who can do nothing; and requires believing in Christ, that it may draw the sinner unto Christ, who has done all things that so the righteousness of the Law may be fulfilled in him. e) How sweetly the Law and gospel do agree in one. . .In this Sinai-covenant, the Law was not administered without the gospel, nor the gospel without the Law; they were indivisibly conjoined, and inseparably married together; becoming a legal gospel, and an evangelical Law; a gospel, full of doing; and a Law full of believing. Hereby God will have us know, that neither God nor man shall lose by substituting the Covenant of Faith instead of the Covenant of Works, but rather both shall gain; God shall gain a better observance of His Law in the second Adam, than He had in the first; and man shall gain a better righteousness in Christ by faith, than ever they had in themselves before the fall. Thus the gospel does not overthrow, but establish the Law, by setting forth Christ the most perfect Performer of the Law.” (Mystery and Marrow, pp775-78).