P OLITICIANS rarely promise to raise taxes, but for the third election in a row, Barack Obama is making the issue a centrepiece of the Democratic campaign.

As a presidential candidate, he vowed to reverse the tax cuts for high earners that were passed under George W Bush, but two years later, after his party's humiliating defeat in the midterm elections, this was revealed to be an empty threat. An energised Republican majority in the House of Representatives pressured Obama into signing a two-year extension: a supposed compromise that looked more like a capitulation.

The tax cuts are due to expire at the end of the year, between the election and the start of a new presidential term. Speaking at the White House, Obama made it clear that he views Republican intransigence on taxation as a political weakness – and a particularly soft spot for his multi-millionaire opponent, Mitt Romney. "Many members of the other party believe that prosperity comes from the top down—that if we spend trillions of dollars on tax cuts for the wealthiest Americans, that that will somehow unleash jobs and economic growth," he said. "I disagree."

When Bush introduced the cuts, Democrats opposed the whole package, but the parties now agree that they should be extended for families earning less than $250,000 a year – a threshold of "middle-class" that must seem reasonable in the salons of Capitol Hill. Everyone, including the richest, will continue to pay federal tax at the lower Bush rate on the first quarter of a million dollars of their income. Obama is proposing to set the top bracket back to 39.6% – as it was under Bill Clinton – from the current 35%.

This would generate $850 billion in revenue over a decade, according to a Congressional Budget Office estimate, although partisans disagree about the fiscal impact. To Barney Keller of the Club For Growth, which advocates limited government and reduced taxes, this is "an infinitesimal amount," compared to the ballooning national debt. Robert McIntyre, of liberal pressure group Citizens For Tax Justice, sees it differently. "There's a lot of money at stake. You're talking about nearly a trillion dollars: that's not nothing," he says.

All agree, however, that the administration's principal motive for drawing a line on taxes is political. A recent Gallup poll showed that 62% of voters believe that "upper-income people" should pay more. One in five respondents said that Romney's huge personal wealth is a reason not to vote for the Republican nominee in November.

The Obama campaign believes that by putting the issue front and centre it can either force Republicans to cave in, or oblige Romney to explain why he deserves a tax cut, when ordinary Americans are struggling. Given that no Republican – not a single member of Congress – has voted for a tax increase in the last two decades, the latter seems more likely.

"It's just class warfare and political rhetoric, not a serious plan for tax reform, to say that you're going to raise rates on the top 2% of wage-earners," Keller says. "It's just posturing. Obama has shown that he's not serious about tax reform or paying down the deficit."

Edward Kleinbard, a law professor at the University of Southern California specialising in tax policy, says Romney is an easy target. "The President is trying to paint the Governor as someone who is extraordinarily rich, whose natural sympathies and instincts lie with the rich, as a man who is remarkably insensitive to the concerns and struggles of ordinary Americans and a man who, were he to win the presidency, would use it to advance the interests of the rich," he says. "The trouble for Governor Romney is that all those things are true."

During the Republican nomination contest, Romney felt impelled to release his tax returns, after a debate crowd jeered his attempt at evasion. He had withheld them through his term as Governor of Massachusetts and an unsuccessful run for the Republican nomination four years ago in defiance of a bipartisan tradition established by his father, George, during his own presidential campaign in 1968.

George Romney made 12 years of his returns public, saying that "one year could be a fluke, perhaps done for show". His son offered just the last two years, in which he paid $6.2 million in federal taxes on $42.5m in earnings, most of it taxed at the lower capital gains rate for investment income.

"The returns are extraordinarily complex," says Kleinbard. "Who exactly is earning what money and what the sources of that income are remain very opaque. There's dead end after dead end." A Swiss bank account appears on the 2010 return but not in 2011. An Individual Retirement Account, limited by law to $2000 of tax-free contributions per year, somehow contains $102m. There are shell companies in Bermuda and the Cayman Islands, testifying to the artistry of a gifted corporate tax accountant.

Romney has insisted there is "nothing hidden" in the years of returns he declines to release, telling a conservative radio host in Iowa: "I don't manage them. I don't even know where they are." His blind trust, handled by his lawyer, Bradford Malt, has invested $10m in a start-up founded by Romney's son.

Democrats scent blood, although none has landed a punch as cleanly as Newt Gingrich. "I don't know of any American president who has had a Swiss bank account," the former Speaker noted. Romney's standard counter to such attacks is: "I pay all the taxes that are legally required, not a dollar more."

The Republican nominee is on more solid ground when he pivots to the economy. "I understand the president's going to try to do anything he can to divert attention from the fact that his jobs record is weak and he has no plan to make things better," says Romney. The anaemic June jobs report, which showed just 80,000 positions added by the private sector – not enough to reduce the unemployment rate from 8.2% – provides a clear opening.

The Wall Street Journal editorial page, an influential conservative mouthpiece, recently worried that Romney is "squandering an historic opportunity" to win the presidency, adding that "the Romney campaign thinks it can play it safe and coast to the White House by saying the economy stinks and it's Mr. Obama's fault." If hiring remains sluggish all summer and into the autumn campaign, as seems likely, Romney may be right.

Although Romney has never used the actual phrase, his campaign can be boiled down to the question that Ronald Reagan posed a week before his landslide victory over Jimmy Carter in 1980: "Are you better off than you were four years ago?" One of the campaign's favourite lines, "Obama Isn't Working," is a direct lift from Margaret Thatcher's successful attack on Labour in her bid to become Prime Minister in 1979, right down to the queue snaking away from the unemployment office on the poster.

OBAMA is surely a more formidable opponent than James Callaghan, and Romney is no Iron Lady, but his campaign enjoys other advantages the Conservatives can only dream of. Last month, he brought in $35m more than Obama. That headline figure vastly underestimates the true fundraising gap, though, because it takes no account of outside groups, powerful "political action committees" known as Super PACs, which may accept unlimited contributions from corporations or individuals.

These organisations disproportionately benefit Republican candidates and lend currency to right-wing talking points. Bush spin doctor Karl Rove's American Crossroads has estimated it will spend $300m over the course of the election. Americans For Prosperity and other groups bankrolled by Charles and David Koch will chip in $400m. Restore Our Future, the PAC most closely linked to the Romney campaign, has $100m at its disposal.

The Democratic counterpart to these groups, Priorities USA Action, arrived late in the game, due in part to liberal distaste with the campaign financing free-for-all ushered in by the Supreme Court in 2010. Obama only gave it his blessing this year and its stated fundraising target is a comparatively pitiful $100 million, no more than enough to match the outlay of a single Republican donor, casino magnate Sheldon Adelson.

Romney's edge also reflects a shift on Wall Street, which backed Obama over John McCain last time around. At a Romney fundraiser held at Revlon heir Ronald Perelman's estate in the Hamptons last weekend, one wealthy donor, Michael Zambrelli, said he had switched sides. "[Obama] has basically been biting the hand that fed him in '08," he told the LA Times. "I would bet 25% of the people here were supporters of Obama in '08. And they're here now."

This is one reason that, for all Obama's tough talk, progressive tax reform is a mirage. There has been no meaningful attempt to close the carried-interest loophole that allows private-equity managers like Romney to pay just 15% tax on their income, from either side. The Obama campaign hearts private equity, too.

"The Democratic party is conflicted because there's so much money at stake," says McIntyre. "It's fear. So much campaign money comes out of Wall Street that they are absolutely scared to death. Which is sad, because you'd think this would be a populist issue, the general public would think it's great to make these billionaires pay taxes, but the Democratic calculation is 'well, yeah, it might be a nice campaign issue but it's going to turn a lot of money against us.'"

Priorities USA Action believes it can inflict damage. Swiftboat Veterans For Truth, the proto-Super PAC that so effectively undermined John Kerry's run for president in 2004 by questioning his Vietnam war record operated with a tiny budget by current standards. When Kerry was photographed windsurfing, Republicans seized on the image to claim that he was a snob. Democrats hope they can get as much mileage out of the recent shot of Romney on his jetski at his $10m holiday home in New Hampshire.

Obama was not slow to draw the contrast, reminiscing about his childhood vacations, travelling "on Greyhound buses, railroads". To win re-election, despite economic headwinds, he must exploit that common touch to the full.

This is borne out by the latest Washington Post/ABC poll, which showed Obama and Romney in a dead heat, at 47% each. This is despite 63% of respondents believing that the United States is on "the wrong track" and a majority having unfavourable views of Obama's stewardship of the economy. He remains the narrow favourite because of his personal advantages: a massive 36% lead on the question of which candidate is more likable, plus a more important, more slender 10% margin on who best understands the economic problems of ordinary Americans. If Romney cannot close that gap, no amount of money can win him the presidency.