I guess this is a dumb question but can they just keep "injecting" indefinitely? Do they have a magical Money Tree or something?
Yeah, the Federal Reserve has a “magical money tree”: the whole reason they exist is to manage the money supply.
That's a lot like saying the whole reason google exists is to help people find information. There are greedier reasons for these organizations to exist.
No it's not.
> There are greedier reasons for these organizations to exist.
Any “greedier reason” for the Fed is a particular application of managing the money supply; it to exists to manage the money supply, independently of whether it exists to do that for the public interest or “greedier reasons”.