Every nation has a currency. The US economy is just as prone to stagnation, deficit, over, and under valuing as any other currency.
See, you used two words in that sentence. One of them is economy, the other is currency. They're related, but they're not the same. The thing that matters to most US residents is the economy -- specifically that it will be growing enough that it's possible to find a job in it which will secure a certain amount of output to secure one's well-being. (Residents saving for retirement benefit from both). The thing that matters to someone who borrow or lend or hold dollars isn't the economy per se, it's the fact that he can use that dollar in the future to buy a predictable amount of goods and services: price stability. (Stability is better than an increase in value of those dollars, because borrowing and lending need to balance each other out... besides, if you really wanted returns you'd find a real investment, not cash.)
The US has flirted with price stability issues in the past (look at the 1970s and early 1980s), but not to the extent that Russia is experiencing right now. Russia has issued additional rubles through the state-backed Rosneft bond offering (a bailout averting a bankruptcy for one of Putin's top cronies) which was the proximate cause of the ruble free-fall, and because of sanctions, falling oil prices, and general economic decline outside of the oil sector, the ability of a ruble to purchase valuable goods and services (like oil) in the future is in question. China, meanwhile, has its own set of currency controls (hence a thriving black market in RMB-USD) and central-bank interventions of a scope and magnitude which make QE and QE2 look small.
So what else are you going to use? Euros? No way, I thought you were worried about stagnation and deficits and stuff. Gold? Oh, yeah, obviously it's been an absolute MODEL of price stability lately, hahahahahahahahahaha... Bitcoin? Makes gold look good. Pounds sterling? Mmmaybe, in a pinch. Then most of the other currencies are on the small side, so it's harder to use them in high volumes.