James Carville has a way with words. In 1992, the ruthless, foul-mouthed Democratic political operative hung a sign on the wall of Bill Clinton's presidential campaign headquarters in Little Rock, Arksansas. It read: "It's the economy, stupid."

Late last year, the "Ragin' Cajun" turned his attention to the re-election efforts of Barack Obama. "People often ask me what advice I would give the White House," he wrote in September, offering his new maxim: "Fire. Indict. Fight." The president should fire the advisers who are offering him the "same strategy and the same excuses", proclaimed Carville. He should indict the bankers and "get angry about the irresponsible actions on Wall Street"; and he should fight the "Republican austerity garbage".

To his credit, Obama seems to be listening. First, he got rid of his chief of staff, William Daley, a former executive with JP Morgan Chase, who had urged the president to avoid open confrontation with both bankers and Republicans. Then he came out fighting on the economy, "pivoting" his focus from deficits and austerity to jobs and growth.

In what the liberal economist Robert Reich called "the most important economic speech of his presidency", in Osawatomie, Kansas, on 6 December, Obama laid out his clearest rebuttal yet to the self-defeating austerity measures pushed by deficit hawks, and defended his fiscal stimulus. Energised and emboldened, he decried the explosion of income inequality and the Republicans' "you're-on-your-own economics". Next came a decidedly populist State of the Union address in January in which he urged Congress to pass his jobs bill, invest in clean energy and increase taxes on millionaires. This week, the White House released its budget proposals for 2012/13, requesting more than $800bn for job creation and new infrastructure, and renewing the call for higher taxes on the rich. Daley's replacement, Jacob Lew, a staunch liberal, was sent out to tour the TV studios and sell the message. "The time for austerity is not today," he told NBC's Meet the Press.

Rhetoric is cheap. But, in politics, rhetoric matters. Contrary to the conventional wisdom, Obama's left-wing economic populism has so far proved effective. Polls show more and more Americans believe that the country is on the right track and approve of the president's handling of the economy. The latest Washington Post/ABC News poll has Obama ahead of Republican frontrunner Mitt Romney among registered voters by 51 to 45 per cent.

Is there a lesson for centre-left politicians on this side of the Atlantic? Specifically, Ed Miliband? Like Obama, Miliband ran as an insurgent, a progressive outsider fighting his party's centre-right establishment candidate. But, like the US president, the Labour leader has since been attacked by disillusioned supporters for being a cautious pragmatist, too willing to embrace conservative narratives – especially on the deficit.

There are small, if telling, signs that Miliband recognises he has to change his consensual approach. Like Obama, he has appointed a new chief of staff, ex-diplomat Tim Livesey, more in tune with his sensibilities. Livesey is said to support the introduction of a French-style wealth tax on the top 1 per cent of earners. It would be a wise move by Labour: voters are fed up of the gap between the rich and the rest. But bashing bankers isn't popular, bleat Tory right-wingers and Blairite retreads. Really? The "Hesteria" over RBS bonuses suggests otherwise, and a recent YouGov poll, for example, found that 63 per cent of voters support stripping honours from other senior executives of bailed-out banks.

Miliband must ignore the siren calls of those, like the Blairite Shadow Defence Secretary, Jim Murphy, who urge him to reject "populism" in pursuit of a mythical "credibility". He has to stand up for the little guy against vested interests. And it isn't enough to be on the little guy's side – he has to be seen with him, too. "People understand who you are by looking at you rather than reading about you," a friend of Miliband's told me last February. "It drives me mad that I can't think of a single iconic picture of Ed since he's become leader." A year on, nothing has changed: there is still no iconic picture or image to suggest that Ed Miliband is, as he claims, the champion of the squeezed middle.

Obama is touring his country; Miliband seems to be touring Westminster. Or, alternatively, the world of think-tanks and academics. The US president, for instance, delivered his Osawatomie speech in a local high school. Last week, the Labour leader gave a speech in Sheffield in which he spoke of the importance of "standing up for the squeezed middle" and "challenging the powerful vested interests". But he didn't give it outside the Sheffield Forgemasters plant, which had its £80m government loan controversially cancelled by the cuts-obsessed Coalition, nor did he give it inside one of the 30 or so Sure Start centres in Sheffield that are on the verge of closure. Miliband's rousing, passionate, populist address was delivered at... wait for it... the Sheffield Political Economy Research Institute at the University of Sheffield. Wonks will be wonks.

All is not lost. With the right combination of populist rhetoric, bold policies and combative advisers, Obama has shown how it is possible to shake off a detached or professorial image. Miliband, too, has his "tribune of the people" moments – but, like the pre-Osawatomie Obama, they are few and far between. The Labour leader often lacks momentum: he went after News International in the summer of 2011, but then went silent on the future of the Murdoch media empire. He took on RBS's Stephen Hester over his bonus and emerged victorious – but has since had little to say about Barclays boss Bob Diamond's bonus or the row over executive pay at Network Rail.

In an age of economic insecurity, Miliband cannot afford to let the right surf the wave of anger and discontent among voters. He has to be prepared to show voters that he is an idealist as well as a realist, a populist as well as a pragmatist. Thanks to the Republicans' inability to settle on a credible candidate, Obama could afford to wait three years before he changed tack. Miliband doesn't have that sort of time.

Stagnation in Europe is proof of how austerity economics has failed; rising growth and employment in America shows us how stimulus spending works. It also offers evidence for the effectiveness of left-populism – and standing up for the little guy. Miliband, like Obama, must find his inner populist.

Mehdi Hasan is senior editor (politics) at the New Statesman and the co-author of 'ED: The Milibands and the Making of a Labour Leader' (Biteback)