Before everything derails: I think the USA would be just fine for quite some time, although it would remain far more decentralised. If secession had been included (we must assume that including it is a given, and something therefore desired) then the question becomes: on what terms? And the answer would be contsted, and as with every single other issue, we'd get a compromise between those who want those superajorities and those re-votes, and the other side, who want 'whenever a majority of Legislature votes for it, BYE'. And the ultimate conditions would likely be something like "the legislature must approve, but following a special election, so the people can weigh in that way" or "the legislature must approve with a supermajority" or "the legislature must approve, and there must be a pleibiscite". Some method that makes it neither exceptionally difficult nor extremely easy.
I assume that some kind of method for settling matters of federal debt will be included. Note that the option of secession makes a high federal debt unlikely anyway. Federal debts were very limited for a long time anyway, only skyrocketing in more recent times. In this 'secession ATL', a situation whereby certain states want to increase federal spending and fund it with a debt, states vehemently opposed can simply threaten secession to ensure they don't get stiffed with the bill... when they secede. (Irony right there.) So again, the threat of secession looming over the federal government will p[robably ensure that the USA stays pretty decentralised, as it originally was.
This does not mean that the USA is somehow doomed. Not by any means. There will be some disagreements about the proper role of the federal government, and the decentralism-minded states will block every centralist proposal, which will ultimately prompt the more centralist states to simply start working closer together on a sub-national level. The fact that slavery isn't threatened means that centralism-versus-decentralism doesn't become north-versus-south to the extent it did in OTL. Because, yes, there was a big component of "states' rights" to the Southern cause, but that mentality had orginally become so tied to the Southern cause because it could keep the federal government from... interfering with slavery. If the federal government is much, much weaker for much, much longer... then not all Southern power-players will be decentralist, and there will conversely be more decentralist tendencies in certain Northern states.
Still, the issue of slavery is going to be an issue, and at some point, one side is going to secede. The South if the North tries to amend the Constitution, the North if the south succeeds in blocking all such attempts. Seems to me that the big fault of the USA's history has always been slavery, and that there's nothing inherently wrong or destructive about secession.