Of all the various signs that a presidential campaign is in trouble – poor poll numbers, lack of funds, a weary candidate responding to events rather than setting the agenda – none is more telling than the sight of politicians from a nominee's own party rushing to leave the proverbial sinking ship.

In the aftermath of the leaked video from a fundraising event, in which Mitt Romney casts 47% of Americans as government-dependent shirkers, Republican Senate candidates Scott Brown, Dean Heller, Linda McMahon and Linda Lingle flatly contradicted his remarks. All four are running in states that lean Democratic and Brown, in particular, is making a virtue of his willingness to break with his party, so disowning Romney was a political necessity.

"The presidential thing is bound to have an impact on every election," said Tommy Thompson, the Republican running for a Senate seat in Wisconsin. "If your standard-bearer for the presidency is not doing well, it's going to reflect on the down ballot." In congressional races across the United States, Romney is perceived as a drag on the ticket who'll damage other republicans running for office.

There has also been no shortage of unelected conservatives willing to kick the Republican nominee while he is struggling. "Romney seems to have contempt not just for the Democrats who oppose him, but for tens of millions who intend to vote for him," wrote neo-conservative Weekly Standard editor, William Kristol. "He's a kind, decent man who says stupid things because he is pretending to be something he is not – some sort of cartoonish government-hater," concluded David Brooks of the New York Times. "But it scarcely matters. He's running a depressingly inept presidential campaign."

A national Pew Research poll seemed to confirm that Romney is in deep trouble. The headline figure, showing him 8% behind Barack Obama, was bad enough, but the details were even worse: voters view Obama more favourably; even amid the damaging chaos of the Middle East, he is still seen as more personally likeable, more trusted on foreign policy and health care and his supporters are more enthusiastic. Romney's once substantial lead on the question of who would revive the economy has evaporated.

The campaign has been unmoored ever since the lacklustre Republican convention in Tampa. A story on Politico – the journal of Capitol Hill – which was critical of Romney's chief strategist, Stuart Stevens, was full of anonymous quotes from his staff, confirming internal recriminations. This was followed by Romney's cynical and factually dishonest response to the killing of the USA's Libyan ambassador, in which he falsely accused Obama of pandering to Muslims.

The video, secretly recorded at the home of financier Marc Leder, capped a miserable week. Romney comes across as arrogant and dismissive of millions of people whose votes he will need. In the most damning clip, he describes 47% of Americans as people "who are dependent upon government, who believe they are victims, who believe the government has a responsibility to take care of them, who believe they are entitled to healthcare, to food, to housing, to you name it". Within an hour of the leak, numerous analysts on the left and right had written off his chances of winning the election.

This was far from a universal response, though. Some Republicans perceived an opening: a chance for a campaign lacking an identity to define itself. Rush Limbaugh, a hugely influential hard-right voice on talk radio, said the video was a "golden opportunity" and "could be a slam dunk" for conservatism. "Let's break down what you just heard," said Sean Hannity, another hard-right commentator, on his Fox News show. "Because everything that Governor Romney said is 100% accurate."

Romney admitted that the comments were "inelegantly stated" but did not back down, suggesting he views government dependency as an issue capable of motivating the Republican base. Reading the latest swing state poll conducted by NBC and the Wall Street Journal, this may not be such a bad strategy: in Ohio only 6% of voters are undecided, in Florida and Virginia just 5%. Obama leads in all three states, but if the Republican party can turn out its supporters more effectively, Romney could still win.

In his hastily-arranged press conference to explain the remarks, Romney noted that he was speaking "off the cuff" in response to a question, but in truth, the idea that 47% of Americans are parasites has been incubating in right-wing think tanks for many years, to say nothing of its origins in Ayn Rand's division of society into "makers" and "moochers" in her seminal hymn to rampant capitalism, the 1957 novel Atlas Shrugged. Chief among these is the American Enterprise Institute, which regularly warns that the US will become "a nation of takers," if the welfare state continues to grow unchecked.

Romney was factually correct: 47% of Americans pay no federal income tax, according to the non-partisan Tax Policy Centre. This is largely because they are too poor, because they are pensioners, or because they are serving in the US military. Most of these "takers" are liable for payroll, state and local taxes, meaning that their average tax burden is 15.3% of their income. In 2010, Romney paid just 13.9% on his income of $21.7 million.

The number of people paying federal income tax has also declined as a result of a bi-partisan effort to provide benefits to low-income families through the tax code, rather than welfare. The Earned Income Tax Credit, the Child Tax Credit and the Make Work Pay credit were all supported by conservatives as an alternative to raising the minimum wage, effectively subsidising the labour costs of corporations.

This has created what Cornell University Professor Suzanne Mettler describes as "the submerged state", in which huge numbers of people benefit from federal assistance without being aware of it. In her research, Mettler asked people whether or not they had ever "used a government programme": 44.4% of social security recipients said no, as did 39.8% of people getting Medicare, 60% claiming the Home Interest Mortgage Deduction, 47.1% offsetting the Earned Income Tax Credit, and so on.

Since 1960, the welfare state has expanded faster under Republican presidents than under Democrats. States with Republican governors consistently receive more than their fair share of federal funds and generate less in tax receipts.

The idea that other people are benefiting from government programmes paid for with your taxes is at the heart of the Tea Party, which could not function as a political force without huge numbers of white pensioners, all of them getting free healthcare and social security. Whether the signs reading "get your government hands off my Medicare" are born of ignorance or hypocrisy, the broader sentiment that government is nearly always intrusive and unwanted is mainstream.

Romney is betting that although every other American family receives some kind of federal financial assistance, few people "believe that they are victims - believe the government has a responsibility to care for them". In a Vanderbilt University study, swing voters were shown the leaked video and asked whether it made them more or less likely to vote for Romney. The results were fairly evenly divided: 24% against to 20% in favour. When respondents were asked if they paid federal income tax, 80% said yes, many of them no doubt mistakenly.

So while the Obama campaign put together an advertisement showing Americans of all ages and races watching the leaked video, tut-tutting or incredulously shaking their heads and pronouncing Romney unfit to lead, the man himself was on Fox News, restating his position in less clumsy terms. "The President's view is one of a larger government," he said. "I think a society based upon a government-centred nation, where government plays a larger and larger role, redistributes money – that's the wrong course for America."

On October 3, the candidates meet for the first of three presidential debates. Romney will go in with nothing to lose, trailing in the swing states that matter and at the helm of a campaign perceived to be in disarray, creating low expectations that could work to his advantage. He demonstrated in the Republican primaries that despite his stiffness, he has formidable debating skills.

In this, he can take heart from John Kerry, who was trailing badly at this stage of the 2004 election, but came back thanks to a strong debate performance against George W Bush. Kerry lost, but only by about 100,000 votes in Ohio. Romney can also remind concerned Republicans that many analysts thought Barack Obama would be seriously damaged as a candidate by the leaked tape of him describing white, working-class Pennsylvanians as "bitter" people, who "cling to guns or religion", but it didn't stop him beating Hillary Clinton to the Democratic nomination.

There are two jobs reports due between now and the election, on October 5 and November 2, both of which are likely to show anaemic growth and an unemployment rate hovering around 8%, providing further opportunities to hammer home the Romney campaign's Margaret Thatcher-inspired slogan of Obama Isn't Working.

"We're going to nuke Barack Obama into radioactive sludge in the swing states in September," Republican strategist Rick Wilson said. "Crossroads and Restore [two wealthy conservative political action committees] will do the same. It's going to be hitting in concert with the terrible economic news, and it'll strike a chord."

On Thursday, the Census Bureau released its American Community Survey for 2011. It showed that median family income dropped again in 18 states, including the swing states of Nevada, Ohio, North Carolina and Florida. The number of families facing severe hardship has increased four years in a row, to the point where 15.9% of the US population lives below the poverty line. There were some encouraging signs – fewer young adults living with their parents, a marginally more robust housing market – but the overall picture was of a painfully slow recovery that is leaving too many people behind.

"When the president took office, 32 million people were on food stamps," Romney told Fox News. "Now that number is almost 50% higher. Now, 47 million people on food stamps. You've got Americans falling into poverty under this president." One in eight families is dependent on this form of government assistance, just to put food on the table. If all of these people voted Democrat, as Romney claims in the leaked video, Obama would win in a landslide. But they don't, and they won't, and this election is far from over.