On the most basic level, the American Recovery and Reinvestment Act is responsible for saving and creating 2.5 million jobs. The majority of economists agree that it helped the economy grow by as much as 3.8 percent, and kept the unemployment rate from reaching 12 percent.

The stimulus is the reason, in fact, that most Americans are better off than they were four years ago, when the economy was in serious danger of shutting down.

But the stimulus did far more than stimulate: it protected the most vulnerable from the recession’s heavy winds. Of the act’s $840 billion final cost, $1.5 billion went to rent subsidies and emergency housing that kept 1.2 million people under roofs. (That’s why the recession didn’t produce rampant homelessness.) It increased spending on food stamps, unemployment benefits and Medicaid, keeping at least seven million Americans from falling below the poverty line.

And as Mr. Grunwald shows, it made crucial investments in neglected economic sectors that are likely to pay off for decades. It jump-started the switch to electronic medical records, which will largely end the use of paper records by 2015. It poured more than $1 billion into comparative-effectiveness research on pharmaceuticals. It extended broadband Internet to thousands of rural communities. And it spent $90 billion on a huge variety of wind, solar and other clean energy projects that revived the industry. Republicans, of course, only want to talk about Solyndra, but most of the green investments have been quite successful, and renewable power output has doubled.

Americans don’t know most of this, and not just because Mitt Romney and his party denigrate the law as a boondoggle every five minutes. Democrats, so battered by the transformation of “stimulus” into a synonym for waste and fraud (of which there was little), have stopped using the word. Only four speakers at the Democratic convention even mentioned the recovery act, none using the word stimulus.

Mr. Obama himself didn’t bring it up at all. One of the biggest accomplishments of his first term — a clear illustration of the beneficial use of government power, in a law 50 percent larger (in constant dollars) than the original New Deal — and its author doesn’t even mention it in his most widely heard re-election speech. Such is the power of Republican misinformation, and Democratic timidity.