The president's whole context, as White House aides have repeatedly pointed out, is that other people including, in some circumstances, government have helped successful people succeed.
Romney, however, has seized on the condensed version of the comment as illustrating that Obama doesn't understand small businesses and their challenges. It's a strategy that seems to be galvanizing conservatives. Last week, Romney's campaign held 18 "We did build this" events in a dozen states featuring small-business owners who say they made their companies what they are without the government's help.
But critics note that while Romney likes to take credit for turning around the 2002 Winter Olympics, which had been savaged by an international bribery scandal, the federal government pumped more than $340 million into Utah, funding about 18 percent of the Games' overall cost. If money for rebuilding Interstate 15 in Utah and adding light rail are included, the federal total rounds up to $1.3 billion.
"Not only has Mitt Romney blatantly taken the president's words out of context, he has done so with brazen hypocrisy," says Ty Matsdorf, a senior adviser with the pro-Obama American Bridge 21st Century super PAC. "Romney claims the Olympics as one of his successful turnarounds, but what he fails to mention is he was only able to do this with a billion-dollar check from taxpayers a far cry from doing it on his own."
Romney's campaign biography says that he "salvaged the 2002 Winter Olympic Games from certain disaster" and touts his revamp of the Salt Lake Organizing Committee and ability to oversee an unprecedented security mobilization for the Games, which occurred less than six months after the Sept. 11, 2001, terrorist attacks.
"No matter how well we did cutting costs and raising revenue, we couldn't have Games without the support of the federal government," Romney says in his first book, Turnaround.
At the time, that assistance earned the wrath of Sen. John McCain, R-Ariz., who now supports Romney's bid.
"What the Olympics Games, supposedly hosted and funded by Salt Lake City, which began in corruption and bribery, has now turned into is an incredible pork-barrel project for Salt Lake City and its environs," McCain said on the Senate floor in 2000.
Former Sen. Bob Bennett, a Utah Republican and Romney supporter, says the whole argument over the "you didn't build that" comment is meaningless, but Bennett notes that there could be no Olympics ever without government help.
Romney, Bennett says, pared down federal requests after taking over the Games' planning and refused in some situations to say that a Utah project was instrumental to the Olympics to cut back on federal investments.
Private sponsorship was the biggest contributor to the Olympics' success, and Romney boosted that by a huge degree, Bennett notes, and government became involved with what it needed to get involved in: security and transportation.
"You can't do it without it," Bennett says. "If you look at the job Mitt did at the Olympics, the thing he can say is that government couldn't have done that."
Romney's campaign pointed out that he inherited a Games $400 million in the red, then slashed $200 million and brought in multiple new sponsors to make up the difference.
In a letter to the federal General Accountability Office, Romney noted that while the federal cost for the Olympics has gone up, it was actually a huge decrease as a percentage of the overall cost from 52 percent of the 1980 Lake Placid Games to 18 percent for Salt Lake City.
Of course, Romney, too, had his own "you didn't build that" moment, one that his opponent's team is glad to point out. In heralding Olympic athletes' accomplishments during the 2002 Games' Opening Ceremony, Romney said that the Olympians "didn't get here solely on your own power."
"For most of you, loving parents, sisters or brothers, encouraged your hopes, coaches guided, communities built venues in order to organize competitions," Romney said. "All Olympians stand on the shoulders of those who lifted them."
That comment made the rounds of television satirists for a couple of days, but it's Obama's remark that seems to be sticking.
Corporate-funded super political action committees have blanketed airwaves in swing states to highlight the president's comments, and Obama himself recorded a spot to try to counteract the firestorm. But it hasn't seemed to help.
"I'm not sure it's working," says Tim Hagle, a political scientist at the University of Iowa, which is located in a swing state where political ads are ubiquitous.
"There's only so much [the Obama campaign] can do; a statement is a statement. Even in full context, the president said without government, you couldn't build your business."
And that, Hagle says, is why the comment is firing up the Republican base.
"If it's catching on, they must see that it has some value," he said. "For a lot of the folks, especially small-business owners who feel under attack because of the tax policies that are in place or have been announced, this is another way of getting at that feeling."
The now infamous "you didn't build it" quote
"If you were successful, somebody along the line gave you some help.
There was a great teacher somewhere in your life. Somebody helped to create this unbelievable American system that we have that allowed you to thrive. Somebody invested in roads and bridges. If you've got a business YOU DIDN'T BUILD THAT. Somebody else made that happen. The Internet didn't get invented on its own. Government research created the Internet so that all the companies could make money off the Internet. The point is, is that when we succeed, we succeed because of our individual initiative, but also because we do things together."
President Barack Obama, July 13 "To say what he said is to say that Steve Jobs didn't build Apple Computer or that Bill Gates didn't build Microsoft or that Henry Ford didn't build Ford Motor Company or that Ray Croc didn't build McDonald's or that Papa John's didn't build Papa John's Pizza. This is the height of foolishness. It shows how out of touch he is with the character of America. It's one more reason his policies have failed.
It's one more reason why we have to replace him in November."
Mitt Romney, July 18
"No matter how well we did cutting costs and raising revenue, we couldn't have Games without the support of the federal government."
Romney in his first book, Turnaround, published in June 2004.
Athletes in the 2002 Winter Olympics "didn't get here solely on your own power. … For most of you, loving parents, sisters or brothers, encouraged your hopes, coaches guided, communities built venues in order to organize competitions.… All Olympians stand on the shoulders of those who lifted them."
Romney speaking to Olympians at the 2002 Winter Games.
Federal government's 2002 Olympics cash infusion
Safety and security operations
Spectator transportation systems
Building, enhancing or operating expenses for venues
Services provided by federal agencies
Other Olympic-related capital projects
Construction of highway projects
Mass transit projects
Source: GAO study