There were really two housing crashes.
The first one happened in 2007, because people bought places they couldn't afford. Well, not unless prices kept rising. See, they had teaser loans they could pay at first, but not later. So when that later eventually came, they needed to refinance into new ones they could still pay. The problem, though, was they couldn't do that once prices fell enough that their homes were worth less than their mortgages, which didn't take much since they were putting almost nothing down. That's because you need positive equity to refinance. So people were stuck. They had no choice but to default.
The second one, though, happened in 2009, because people who used to be able to afford their homes couldn't once they lost their jobs. In other words, the housing crisis begat an unemployment crisis that begat an even worse housing crisis. Only the government could stop this vicious circle. It had to help the unemployed so they could stay in their homes. And it had to stabilize housing — along with the rest of the economy —s o more people wouldn't lose their jobs.
That's what the government stimulus did. Indeed, a new paper by Joanne Hsu, David Matsa and Brian Melzer, finds that unemployment insurance (UI) alone prevented about 1.4 million foreclosures between 2008 and 2012. They were able to calculate this because different states had different benefit levels. So, controlling for each state's economy, they could observe how much increased UI reduced mortgage delinquencies. And, as you can see below, the answer is quite a bit: States with more generous benefits tended to have lower default rates.
Here's a bit of perspective: Unemployment insurance stopped almost twice as many foreclosures as the administration's anti-foreclosure program, HAMP, which prevented only about 800,000. And the good news didn't stop with keeping families in their homes. It also kept spending from falling into an even deeper downward spiral, because it gave the unemployed money directly, and, critically, kept credit flowing to them, since they didn't default like they otherwise would have.
In short, the best stimulus is helping people who need help the most. Somebody tell some Republicans.