On 17 July, President Barack Obama spoke at a campaign rally in Roanoke, Virginia. It was a typical event for an incumbent president who is seeking a second term. In his remarks, he offered his vision of government's role in spurring entrepreneurship and creating jobs in the United States:

"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."

This is all fairly boilerplate rhetoric – a basic recitation of how Democrats view the role of government and its interplay with the private sector. But in this statement, there was one phrase that Republicans have grabbed on to like a famished dog with a new bone:

"You didn't build that."

That single phrase, taken out of context by Republicans, has become the GOP's symbol of Obama's supposed contempt for the free market and entrepreneurship, and for his socialist assault on America. Sure, it's a misleading lie to cast it that way. But in the hands of Republicans intent on furthering their vision of the free market as a fragile institution whose success relies on as little interaction with the federal government as possible, it quickly became a stand-in for all that is wrong with Obama.

And so, the Republicans made "We built that" the theme of Tuesday's convention proceedings. Speaker after speaker hammered on this theme, accusing Obama of disrespecting small business. But they did so with almost a wilful sense of hypocrisy. For example, Delaware lieutenant governor candidate Sher Valenzuela attacked Obama for the line despite the fact that, just a few months ago, she gave a detailed speech to a business group about how they could do a better job getting government contracts.

The shining example, however, was Phil Archuletta, a New Mexico businessman whose business makes outdoor signs – in part, for the federal government. Archuletta's chief complaint against the president was that Obama's stimulus bill had made it harder for him to win government contracts – an odd message for an evening dedicated to the notion that small businesses need government to get out of the way.

Democratic partisans were busy tweeting out the fact that Obama has signed multiple pieces of legislation providing tax breaks for small businesses, but such "facts" simply bounce harmlessly off the GOP's protective truth shield. Indeed, if there is one overarching takeaway, not only from the sessions so far at the Republican convention, but also from the last year of political campaigning, it is that Republicans not only toil in their own narrowly and misleadingly constructed world, but really are just making stuff up.

There were plenty of instances on display last night, beyond the "you didn't build it" meme. The most pernicious and racially-coded example is the oft-repeated claim by the Romney campaign that Obama, by granting waivers to states, has gutted the work requirement of the welfare reform bill (passed more than 15 years ago). The charge has become a crucial element of Romney's attacks on the president, even though, as many independent fact-checkers have pointed out, it simply isn't true. It's another lie; and yet, it was repeated last night by former Democratic Congressman Artur Davis, and again, by failed presidential candidate Rick Santorum, who went a step further and accused Obama of creating a "nightmare of dependency".

These are the big lies; but there are so many other ones that it's almost impossible to keep track. For example, speaker after speaker denounced Obama for running up $5tn in debt. While budget deficits that have increased the national debt have occurred during Obama's presidency, only someone who believes history began on 20 January 2009 (when Obama took office) can think he is fully responsible.

As this handy chart, put together by the folks at the Center on Budget and Policy Priorities, the debt is a result of a confluence of factors: the Bush tax cuts, the wars in Iraq and Afghanistan, the decline in tax revenue from the economic downturn, Tarp, and – very slightly – recovery measures put in place by President Obama. Republicans have completely washed their hands of any role and any responsibility for America's ever-increasing red tape – and it should be noted that the budgets of both Romney and Ryan (when he served in the House) would, because of massive tax cuts, further explode the deficit.

Republicans also decry the president's jobs record and they certainly have a point, but again, to blame Obama for 8% unemployment is to ignore the fact that Congress exists: it has regularly blocked any and all job creation measures ever since Obama's stimulus bill, which did create about 2.5 million jobs.

Then, there are assertions like keynote speaker New Jersey Governor Chris Christie's claim that Americans are "overtaxed", even thought the tax burden on taxpayers is at its lowest point since the Truman administration – and Obama has repeatedly cut taxes as president. Indeed, as Tom Schaller, a political scientist at the University of Maryland, Baltimore County (UMBC) said to me:

"Republicans say they value low taxes and hard work but fought until the 11th hour against the only tax levied directly on work: the payroll tax."

But all of this is at pace with a conservative worldview that considers government to be nothing more than malevolent interference with the smooth operation of the private sector – except when it's not. "Jobs don't come from government," said Texas Senate candidate Ted Cruz last night, a view that basically sums up GOP economic thinking. But if you listened to Republican governors on Tuesday, you might have found yourself surprised to discover that, in their states, the government has played an oddly integral role in spurring job creation. If you listened to Mary Fallin, governor of Oklahoma, extol the virtues of the energy industry in her state and bemoan "more government, bigger spending and more regulation", you might never know that the oil and gas industry is deeply reliant on – and spends millions lobbying for – tax breaks from the federal government.

One can believe that government should play a less direct role in the workings of the private economy – clearly, this is a defensible notion. But to listen to Republicans harping on Obama's "you didn't build that" line is to hear a party that views "government" in the most simplistic imaginable terms. This isn't a governing philosophy; it's a caricature of how the economy actually works.

To be sure, it's hardly unusual for political rhetoric to take liberties with the truth, or to stretch an argument to breaking-point, but with Republicans today, the issues runs much deeper. Very simply, the way they talk about what the federal government does or should do, and about the role of spending, taxation and regulation, is more than just a compendium of lies: it describes an alternate reality.

In the GOP's defense: at least they can argue they built that.

• Editor's note: this article originally identified Mary Fallin as governor of Nebraska; this was amended to Oklahoma at 12.30am on 30 August 2012.

• This article was further amended on 3 September 2012 to clarify Thomas Schaller's affiliation.