The problem is, the economy would have recovered if the government had done nothing.
The economy is natural and organic. It doesn't require the government to do anything at all, for the economy to grow and expand.
Does the government have to come and tell you:
"Hey! You would really like to buy something! You need to go to a store, and purchase something"?
Nope.
Does the government go to people who produce stuff, and say:
"You know, you really should come up with a product people want to buy, and then sell that product"?
Have you seen a government agent yet, go to a retail shop owner and say: "You know, if you purchased some products from suppliers, you could sell those products for a higher price at a profit, and that would be good"?
Of course not. Every fundamental aspect of the economy happens without a single government regulation, or stimulation, or mandate.
People naturally without any external motivation, like to buy things. People naturally like to produce and sell stuff.
Both of these things would happen without any government at all.
When you see "jobless claims lower", and imply that the government had something to do with that, shows only an ignorance of how the economy functions.
There are only two ways government can directly lower jobless claims. First they can lower the benefits of jobless claims, thereby giving greater motivation to get a job. Second they raise the requirements to make a jobless claim, thereby reducing the number qualified, and thus the number using the system.
There is a third, but it's a game of smoke and mirrors. They can hire more government employees. But the problem there is, for every dollar in wages given to a government employee, a dollar plus must be confiscated from private employees. Thus, every job created, destroys multiple jobs in the private economy.
Therefore, reducing jobless claims, although being a good thing, does not by any stretch indicate that government has done anything to fix the economy.