First of all, we must note that it is impossible to know for sure if the government's policies did stabilize the economy. We know that the economy did stabilize to an extent, but we do not know for certain what caused this to happen.
In theory, the government stabilized the economy through Keynesian fiscal policies. The government did two major things in fiscal policy. First, it created a stimulus package. This consisted of large amounts of government spending. Second, the government continued to keep taxes low, in some cases creating new tax cuts. Both of these actions were meant to stimulate demand. The idea was to make sure that people had more money to spend. As the people spent the money (the theory goes) aggregate demand increased and the economy stabilized.