If you mean the people of the US still value the dollar, i don't think it would be a huge hit.
People will scoop up all the free dollars, and bring them back to the us where they have value.
Contracts still have to be paid in dollars. Some people around the world would be upset that their dollars are worthless, but it turns out they could sell those dollars to people who need to pay debts in dollars. So suddenly this valueless piece of paper has value again, because you can trade it for things you want.
if you can in an instant impose some irrational condition for an instant, i think the global economy will, certainly shift, but people would notice all of the arbitrage opportunities and things would _generally_ go back to the way they were, like a flash crash.
if you could wave a magic wand, and make people think the dollar is worthless for 10 years? That would be weird. i imagine we'd make a new currency, dollar2 and just pay everyone in that. you could bring in old dollars to the us and exchange them for dollar2's. But because people are under a spell, they can't think of the arbitrage idea. so it only happens accidentally.