Philadelphia in September 1787 was as deliberate a product of design as a foundational political charter can be. 
Its drafting and adoption were preceded by extended debate among the delegates to the Constitutional Convention and prompted heated advocacy and counteradvocacy by federalists and antifederalists, and its provisions were debated anew in ratifying conventions in each of the thirteen sovereign states. On numerous levels and including numerous parties, then, the U.S. Constitution incorporates and derives its authority from acts of consent. 
It is not mistaken to think of the constitutional founding as putting flesh on the theoretical bones of contract theory. The Constitution's liberal provenance is undeniable, especially when the Bill of Rights is also taken into account. The Constitution is not, however, the child of only one parent. In important respects it also descends from covenant theory. That other heritage goes a long way toward explaining, I believe, both its sturdiness and the esteem in which it continues to be held. 
In one respect, the American Constitution is the antithesis of Israel's covenant: it displays itself as an entirely human contrivance. Indeed, its thoroughly secular character bears remarking. Should we imagine the United States preparing a similar document in the early twenty-first century, we would expect it to contain somewhere an effusive peroration to a benign providence or a plea for divine guidance. Their absence in the eighteenth-century document is a function of the uniquely rationalistic character of that phase of the American experience. In other respects, however, the Constitution bears more resemblance to the Sinai story than it does to Lockean contract. 
Not only chronologically is it maximally distant from the Mayflower Compact on one end and Billy Graham's revival meetings on the other. 
Most obviously, the agreement is neither hypothetical nor indefinite. The manner in which its terms are debated and approved is a matter of public record, and all parties to it are identifiable. Among them are the thirty-nine signers, but they are not proceeding on their own authority. Rather, they act on behalf of the states for which they are delegates. This constitution is a compact uniting those states, but, as the preamble makes explicit, it is not the states as such but rather the totality of the people who "ordain and establish" the union. 
A people is, of course, too numerous and dispersed for each citizen to be active in designing and approving the instruments of a new government. There could be grounds for suspicion, then, that their imprimatur is being invoked as cover for the real actors. Allaying this concern are several related factors. First, the people are represented by the most respected and distinguished of their compatriots, arguably the most accomplished assemblage of Americans ever to occupy a room together. Their probity is exceptional. If these men cannot be trusted to transact the public business, it is hard to see who could be. Second, the Constitutional Convention's product is then taken back to the several states for ratification. It is discussed at a higher level of sophistication -most notably in the Federalist Papers -than political discourse has ever subsequently been afforded on the continent. Citizens know what they are being offered and have access to illuminating and principled arguments for and against. The state conventions in which the ratification question is debated are responsive to the citizenry they represent. Approval is not by the unanimity that Israel allegedly offered up at Sinai, but it comprehensively engages public reason. This is indeed a mechanism o