No Congress can not, the Federal Reserve can, which is not under the authority of congress at all really.
Congress can spend money, and Congress can Mint Coins (i.e this story) but it can not create federal reserve notes
If it spends more money than it take in from taxes it must issue Treasury bills that is has to sell to someone, Today almost no one wants to buy US Debt because congress is irresponsible like a child with a AMEX Black card.
So the only entity willing to buy US debt is the Federal Reserve who does so by money printing aka inflation of US Currency aka a tax on responsible people in society
They damn well can. There's nothing stopping congress from dissolving the federal reserve tomorrow if they'd like, other than the general dysfunction of congress that's spurred this whole discussion.
This seems to be the premise of a lot of later conclusions you're making, but it's basically wrong: Congress can print money at will. The debt ceiling is not the reason we don't do that. Reputation and inflation mostly are.