The US dollar is a promise that you can redeem it - for dollars.
Exactly, a dollar is a bearer bond that can extinguish a Dollar of DEBT, debt in the form of taxation is a big part of that, but also legal tender laws mean ANY private debt can also be extinguished by the dollar. So the dollar is the universal extinguisher of all debts in the U.S. and that is it's backing.
I've argue in other threads that the BTC computer network or even the cryptographic code of BTC dose not constitute backing for BTC, because it dose not establish any price or valuation for BTCs. Instead all they do is try to provide limited security against theft, and prevent counterfeiting. So while users can have some assurance they will still posses their BTCs in the future and that BTC will still be rare, theirs no guarantee they will be high priced in the future.
Also in response to an earlier statement that 'all goods exchanged or offered for sale for BTC' are a backing, this wrong for two reasons. First all such merchants are free to remove these offers at any time, and second not one single merchant on Earth actually sets prices IN BTC itself, they always make use of the exchange rate and thus they do not act to fix a value for BTC because you can have no confidence that any quantity of coins will ever buy any amount of merchandise.