The Confederate States of America went into debt to finance their war of secession. After the war some of their creditors wanted that debt repaid. The United States, on the other hand didn't want them to recover any of their investment, for the obvious reasons. In response to the insistence that this debt not be paid, sympathizers of the Confederacy suggested that, likewise, the debt of the Union should not be paid, for the obvious reasons. Additionally, it was argued that the emancipation of slaves was a taking of private property, so that, under the Fifth Amendment, former slave-owners were owed
The North reminded the South who was making the rules, and included the following as section 4 of the Fourteenth Amendment:
The validity of the public debt of the United States, authorized by law, including debts incurred for payment of pensions and bounties for services in suppressing insurrection or rebellion, shall not be questioned. But neither the United States nor any State shall assume or pay any debt or obligation incurred in aid of insurrection or rebellion against the United States, or any claim for the loss or emancipation of any slave; but all such debts, obligations and claims shall be held illegal and void.(Underscores mine.)
There's probably someone out there somewhere, even now, insisting that the debts of the Confederacy should be repaid, or that descendants of slave-holders are owed reparations, but those issues no longer have much currency, nor can they be expected to recover currency.
On the other hand, when addressing the debts of the United States, that Amendment included but did not limit itself to those debts
incurred for payment of pensions and bounties for services in suppressing insurrection or rebellion. What remain potentially relevant, then, are the underscored words:
The validity of the public debt of the United States, authorized by law, […] shall not be questioned.The
nationaldebts of the United States cannot Constitutionally be repudiated, without further Amendment. Under the Constitution, they have to be serviced; and, when they come due, they have to be paid.
Present levels of deficit spending are widely seen as unsustainable, and the United States Treasury has begun to pay discernible risk premia, which is to say that a significant part of the market expects that the United States might default. So one question is of how a default might be effected.
In theory, an Amendment could quickly be ratified to permit default, though a significant share of the
national debt remains domestically held, which would tend to brake the passage of such an Amendment. Of course, the beginning of the process of amendment would drastically erode confidence in the debt, so that the risk premia would grow dramatically, and the Treasury might find itself almost immediately unable to pay bills, and might remain unable to do so until the Amendment were ratified and restructuring negotiations were completed.
A more likely process would be a Declaration of Emergency, under which the Constitution were
suspended, as the federal state worked-out what it could expropriate from whom. (The Constitution makes absolutely no provisions for such emergency suspensions, but we've had a long history of our rulers claiming the power to effect them, and of courts doing little to check such actions.) Again, the United States might be unable to borrow money, but the process of partial repudiation could immediately be brought forward.
Or it might be that the debt were restructured without the consent of creditors. Such a restructuring would, in fact, be a partial repudiation, but lawyers and judges have long proved adept at making distinctions where there are no differences.
 With one exception, during each war since the adoption of the Constitution, the President has
suspended provisions of the Constitution. That one exception was Madison, who had been the principal author both of the Constitution and of the Bill of Rights.