Article IV, Section 1 of the United States Constitution, known as the "Full Faith and Credit Clause", addresses the duties that states within the United States have to respect the "public acts, records, and judicial proceedings of every other state."
As currency is legal tender/promissory note ... Full Faith and Credit in this case refers to universal acceptance of USD by all states. It also defines that the currency is not based upon any intrinsic or tangible value.
Similar to Bitcoin ... the value of Bitcoin is purely based upon what other will pay for it without regard to collateral or credit/payment/value history of any kind other in and of itself. The value of floating currency has no real/tangible collateral or assets only the "Faith and Credit" of the issuer.
My memory is not as good as it use to be, so I had to go back and read it a couple of times, but the "full faith and credit clause" appears to cover the legal proceedings of one state to be recognized in another state. IE: you convict someone of a crime in one state, they couldn't flee to another state and have the judgement set aside. It also deals with the right of the US government as the trustee of the people to transfer property. I think it would be a really long stretch to say it guarantees our current dollar.
I was reminded of something though and I suspect you are confusing the current Federal Reserve Note of today with US Note (Greenback) of yesteryear. The currency act of 1862 allowed the US Treasury Department to issue US Notes, which were in fact guaranteed by the US Government. They were officially discontinued in 1971, but there are some still in circulation.
The current Federal Reserve Note we use isn't issued by the US Government, it is issued by the Federal Reserve Bank under the provisions of section 16 of the Federal Reserve Act of 1933. They are as such liabilities against the assets of the Federal Reserve and member banks of the Reserve. The Federal Reserve Banks are not a part of the US Government but were authorized to exist by the 1933 act to provide banking services (issue paper money), and are private corporations. Technically because they were authorized by Congress their obligations ultimately are the obligations of the US Government, but if the banks were to fail, there would be no way to collect anyhow. Something that almost happened not that long ago, remember the "to big to let fail" reasoning under Bush on bank bailouts, but that's another story.
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