I was tooling around Quora last night and came across a question that I think a lot of people have: “Why do some people insist that the $787B stimulus package wasn’t big enough?”

In general, I think this question tends to get answered the wrong way. The typical response is that Christina Romer initially estimated that we needed a $1.2 trillion stimulus, but then the political team shaved it down to $800 billion, and that’s where the mistake was made. But Romer’s estimates — which were based on private-sector estimates — came before we knew the real size of the recession. A world in which Congress followed Romer’s advice is still a world in which we did much too little, because Romer’s calculations were completed before we knew how bad the recession really was.

The Obama administration has taken a lot of heat for predicting (pdf) that the stimulus would keep unemployment from rising above 8 percent. But I’ve always thought the more important information on that chart was the line tracking what would happen if the stimulus didn’t pass. The Obama administration had some reason to offer a rosy estimate of a world with the stimulus bill, but they had much more reason to offer a doomsday prediction of a world without a stimulus bill. With that in mind, look again at the infamous chart that Christina Romer and Jared Bernstein worked up to project the effects of the stimulus in January of 2009:

As you can see in the graph, that line peaks at the end of 2009, when unemployment hits 9 percent. Back in the real world, the Bureau of Labor Statistics estimates that unemployment hit 10.1 percent in October of 2009. This was before the stimulus began spending the bulk of its money. So whatever you think of the Recovery Act, the administration’s worst-case scenario was far, far too rosy. As a matter of logic, that implies that the policy response — which was already much weaker than they wanted it to be — was far, far weaker than the situation called for.

Given what we knew, we were doomed to start with an underpowered stimulus. But we weren’t doomed to a continually underpowered stimulus. The way this is supposed to work is that we do the best with the data we have and then update our efforts in response to the data we get. But that’s where things really broke down. The error wasn’t just that the original stimulus was too weak. That was unavoidable given what we knew when it passed. It’s what happened — or, more to the point, didn’t happen — when we learned that we hadn’t done enough.

In fact, it’s worse than that. The underpowered stimulus ended up discrediting itself because it didn’t live up to the Obama administration’s (faulty) projections, and instead of realizing we needed more, the fact that we were still seeing tremendous joblessness gave the opposition party an opportunity to argue that we needed less. It’s as if we took too few antibiotics, and finding the disease still present, decided to give up on antibiotics altogether.

That still leaves the question of what an appropriately sized stimulus would have been. I posed the question to both Romer and Bernstein, and they gave me the same answer: The stimulus needed to be bigger, but even putting politics aside, it would’ve been hard to make it bigger.

“A rough, back-of-the-envelope calculation is that $100 billion of stimulus creates 1 million jobs for 1 year (or reduces the unemployment rate by about 1/2 percentage point for a year),” Romer told me over e-mail. “So, if we needed to reduce the unemployment rate another 2 percentage points for two years, we needed about another $800 billion. So, we probably needed about $2 trillion given what we were actually up against.”

The problem, she says, is that more stimulus also means more problems designing the stimulus. “We had a hard time spending $800 billion quickly,” she says, and “with that much stimulus, the issue of diminishing returns could be important. We don’t have much experience with something that large, so I am less confident that the same multipliers would hold.” Perhaps making things even harder, “that much stimulus would have been irresponsible just on its own with no plan for paying for it. It could well have spooked financial markets. If we were going to go that large, it would have had to be with an explicit agreement on what taxes would be raised or spending cut in the future to pay for it.” Passing such a deal would’ve been almost impossible amid the crisis environment of 2009.

Bernstein’s calculation proved very similar. “The simple Keynesian answer is you take the GDP gap— actual GDP minus potential— sum it up over the downturn, and divide by the multiplier,” he wrote to me. “Using annual CBO potential GDP and the real GDP on the books for 08-2010, you come up with a GDP gap of around $3 trillion. Divide that by 1.4, and you’d need around $2 trillion, more than twice the ARRA.”

But, like Romer, he thought the abstract calculation a lot easier than the practical problems associated with shoving $2 trillion into the economy in a fast, effective fashion. “That $2 trillion ignores implementation constraints,” he continued, “which are also binding. I don’t believe we could have efficiently and effectively put that large a stimulus to good use with requisite accountability.”