Even with all the money being printed by Fed (>80 billion usd per month!) there is not enough money for the biggest military+police government on Earth.
Without going into the details... you know that the Federal Reserve doesn't pay the bills, right? The Treasury does. And when the Treasury pays the bills, it doesn't really have much to do with the Fed buying bonds on the open market. The Treasury pays bills based on interest on national debt, stuff like social security and spending approved by congress. For some reason, congress implemented laws which mean that they have to give permission to the Treasury to pay the bills that congress itself voted into the budget.
My point is that this whole debacle doesn't really have to do much with the Fed, and the Treasury is just following the orders of congress.
*Edit:
Ah, I see from stalking your profile that you are not American. Well I can see why you'd be confused - shit's confusing. I don't think even most US citizens understand how it works.
You have a lot of things mixed up. This isn't about not enough money. It's about Congress having to pass a budget in order to run the government. Maybe you're thinking of the debt ceiling?