Some assumptions about President Barack Obama’s stimulus package don’t hold up. Here are a few.

• Assumption: “Obama’s Stimulus Package Was an Epic Failure that Haunted His Presidency.”

No. President Barack Obama’s $787 billion stimulus bill was certainly a political failure. Obama signed it during his first month in office, cutting taxes for more than 95 percent of American workers, while pouring cash into health care, education, energy, infrastructure, and aid to victims of the Great Recession. It was textbook Keynesian economics, using public dollars to revive private demand, but within a year, the percentage of those who thought it had created jobs was lower than the percentage of Americans who believe Elvis is alive.

Nearly four years later, the bill – and the tepid economic recovery that followed it – is at the heart of the debate over Obama’s campaign for a second term. To his Republican challenger, Mitt Romney, the stimulus was a big-government boondoggle that blew up the national debt without putting Americans back to work. Obama argues that the American Recovery and Reinvestment Act saved the country from a second Great Depression, ending an economic nightmare in the short term while laying the groundwork for a more competitive and sustainable economy in the long term. .

The facts are on Obama’s side.

There is voluminous evidence that the stimulus did provide real stimulus, helping to stop a terrifying free-fall and avert a second Depression. America’s top economic forecasters – Macroeconomic Advisers, Moody’s Economy.com, IHS Global Insight, JPMorgan Chase, Goldman Sachs, and the Congressional Budget Office – agree that it increased GDP at least 2 percentage points, the difference between contraction and growth, and saved or created about 2.5 million jobs.

• Assumption: “Obama Promised to Keep Unemployment Below 8 percent.”

Not really. In early January 2009, the incoming president’s transition team did release a politically disastrous report warning that the jobless rate could hit 9 percent without the Recovery Act, while predicting it would stay below 8 percent with the Recovery Act. The report was cluttered with caveats about “significant margins of error” and such. Nobody remembers caveats. Unemployment passed 8 percent before the stimulus money even started to flow.

• Assumption: “The Stimulus Should Have Been Bigger but Obama Wimped Out.”

Yes and no. While Republicans have been trashing the stimulus as big government run amok, more liberal critics have dissed it as ludicrously small. And it’s true: More stimulus would have closed more of the output gap and replaced more of the 8 million jobs lost in the Great Recession. More tax cuts would have injected more money into the economic bloodstream. More public works would have created more jobs. More aid to states would have prevented America’s governors from offsetting the Recovery Act’s impact by raising taxes, laying off teachers and other public employees, and slashing Medicaid and other services. Their spending cuts and tax hikes pulled almost as much money out of the economy as the stimulus pushed in.

Even so, the common belief among liberals that pumping inadequate stimulus into the economy was Obama’s original sin is ahistoric and unfair. The Recovery Act was still massive – the latest estimate is $831 billion, larger than the entire New Deal in constant dollars – and it wasn’t Obama’s fault it wasn’t bigger.

Republicans had decided to oppose the Recovery Act en masse. Obama did end up squeezing another $700 billion of stimulus out of an extremely reluctant Congress, through a dozen separate bills. But it wasn’t easy.

• “Unlike the New Deal, Obama’s Stimulus Won’t Leave a Lasting Legacy.”

Wrong. This is the biggest misconception, and it’s because it was marketed as a jobs bill. But it was about reinvestment, long-term transformation as well as short-term stimulus.

For starters, the Recovery Act was the biggest, most transformative energy bill in history, financing unprecedented government investments in cleaner coal, energy efficiency, , advanced biofuels and the refineries to brew them, and factories to manufacture all that green stuff in the United States. The stimulus was also the biggest and most transformative education reform bill since the Great Society, shaking up public schools with a “Race to the Top” competition designed to reward innovation and punish mediocrity. It was a big and transformative health-care bill, too, laying the foundation for Obama’s even bigger and more transformative reforms a year later. It included America’s biggest foray into industrial policy since FDR, the biggest expansion of anti-poverty initiatives since LBJ, the biggest middle-class tax cut since Ronald Reagan, and the biggest infusion of research money ever. Its main legacy, like the New Deal’s, will be change.