I actually think we could have limped along on the basis of the Articles, with a couple crucial amendments:
1) permit a Continental standing army and navy;
2) legally bind the states to pay their allocated taxes to the Continental Congress.
The Articles for "The United States In Congress Assembled" had a pretty interesting approach to apportioning taxes by the way; Congress was supposed to assess each state's overall economic worth, and hit each state up proportionally to that assessment--rather than either the head tax of the OTL Constitution (never enacted) nor the modern income tax. It seems kind of cool to speculate how that might have worked if the system had shaken down being really operational. It would of course be up to each state to figure out how to raise the money to pay the Congressional assessed tax.
For those who have not dived into the format of the Continental Congress, it is important to stress that each state had in effect one vote; different states sent different numbers of delegates, but this was at their option, and the members of each state delegation were supposed to agree on a single vote for their state on any issue. I think sooner or later the strain of such an undemocratic approach would somehow or other snap the system; either a reform would allow either straight proportionality of voting strength to state population or some compromise formula (square root of the ratios, say) or the union would break down I suppose. But the longer the Articles remain in force, undergoing occasional modification to be sure, the more the USA would in fact shift from a dozen or two states attempting to be sovereign nations in an alliance of convenience toward being in fact one unitary nation that happens to be subdivided administratively.
I actually reject the idea that the 13 colonies in rebellion becoming states were in fact separate sovereign nations; amazingly, one of the provisions of the Articles is that a citizen of any state in the USA could relocate to and settle in any other state, and in due time this host state would have to accept the immigrant as a citizen on an equal basis with any other state citizen (of the same general qualifications anyway) who happened to be born there. This is a straight carryover from the status of the many colonies before the Revolution of course; a British subject who was born in say Bermuda could of course relocate to Massachusetts or New York or South Carolina--or to Blighty itself for that matter. Before the revolution, all the colonies that ultimately made up the USA originally were thus not sovereign, but autonomous branches of a single larger, one might say federal, polity. I hold the USA upon its formation took up this role and the various former colony states each accepted in fact that they were properly speaking really part of the larger whole, with commonalities between them making the idea of optional secession absurd. Of course this was not well and consciously realized, but it remains true the USA was in fact one sovereign state by its nature, however we might choose to organize the federal level.
So--one option in case of major misfire of the Philadelphia plan is to just fall back on the minimal and obviously necessary provisions to give Congress the means to actually collect the taxes they resolved in theory to levy, and the right to organize military force to collectively defend the USA. Given those two powers, I think the Articles regime could limp along with pragmatic revisions as necessary in a largely workable way, and the general commitment of Americans to making the larger USA work somehow would allow an evolution from the Articles as they existed in 1786; over hundreds of years, and a probable Civil War, a lot of evolution would take place, but consider for instance what a difference such Amendments as the Reconstruction Amendments or direct election of Senators or women's suffrage makes between our current Constitution and that of 1787.