The 14th Amendment sort of guarantees that American debts including debts for American dollars will be paid by the US.

What backs up the idea that bitcoins have a certain or any value? The word of someone you don't know?

In that way, it's no different than the US dollar or any other "real" currency. This year, Argentinian and Venezuelan currency have illustrated that paper money is a kind of magic act.

Bitcoin wasn't designed to have a stable value (although it doesn't work as designed if the value is wildly unstable, as it is now). It's supposed to be an anonymous, unregulated means of exchange. When the value swings wildly, people stop using it as currency and instead use it as a means of speculation.

Section 4.

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.

https://www.law.cornell.edu/constitution/amendmentxiv

The US taxpayers guarantee they will pay the public debt. Our money is printed and backed by the US government, by our tax money.

That is why this tax bill is such a terrible thing. The Republicans are gambling that trickle down economics will work. They are giving away far too much money to far too few people and gambling far too much on their scheme.

If we can't compete in the world and take care of the American people, then we need to reform more than our tax system. We need to reform our society, the way we care for each other and the poor, and a lot of other things.