There aren't many actual piles of money anywhere, certainly not trillions. It's all invested in something.
And dollar bills are not more substantial than Treasury bills.
Insolvent, to me, means they can't pay current bills, and they can, and do. But I suppose all this is just terminology. The main thing is they can still pay about 75% of their obligations even if nothing is done, and nearly everyone expects Congress to "do something" somewhere along the line.