Neither of these things is happening. In fact, quite the opposite.
It's true that there's been a lot of new Federal debt, but such is the scramble for low-risk assets like Treasuries that their prices are now soaring, which drives yields down. At this point, the interest rate on Treasury securities is so low, buying them amounts to a deal where you give money to the Treasury and they promise to give it back, plus a minimal amount of interest. Then again, considering the other possibilities on offer which might not pay you back, that's a pretty good deal right now.
In order to buy Treasury securities, you have to have dollars, so demand for dollars has been strong. And however bad things look here, chaos overseas means that things don't look any better elsewhere. All of this has meant that the dollar is gaining lots of ground on the euro. The euro dropped below $1.35 during the day today, down from around $1.60 in mid-July.
How long will this go on? Who knows? It wasn't really expected to go this way to start with.