Of all the myths and falsehoods that Republicans have spread about President Obama, the most pernicious and long-lasting is that the $832 billion stimulus package did not work. Since 2009, Republican lawmakers have inextricably linked the words “failed” and “stimulus,” and last week, five years after passage of the Recovery Act, they dusted off their old playbook again.

“The ‘stimulus’ has turned out to be a classic case of big promises and big spending with little results,” wrote Speaker John Boehner. “Five years and hundreds of billions of dollars later, millions of families are still asking, ‘where are the jobs?’ ”

The stimulus could have done more good had it been bigger and more carefully constructed. But put simply, it prevented a second recession that could have turned into a depression. It created or saved an average of 1.6 million jobs a year for four years. (There are the jobs, Mr. Boehner.) It raised the nation’s economic output by 2 to 3 percent from 2009 to 2011. It prevented a significant increase in poverty — without it, 5.3 million additional people would have become poor in 2010.

And yet Republicans were successful in discrediting the very idea that federal spending can boost the economy and raise employment. They made the argument that the stimulus was a failure not just to ensure that Mr. Obama would get no credit for the recovery that did occur, but to justify their obstruction of all further attempts at stimulus.