In the runup to the inauguration of its first president, the republic of the United States was engaged in an earnest debate over how to address its new leader. After a month the joint congressional committee on titles came up with: "His High Mightiness, the President of the United States and Protector of their Liberties." By some accounts George Washington was more than happy, but others feared that it smacked too much of the deferent, monarchical culture they had just deposed. After much discussion they agreed on "Mr President" – ensuring that for all the trappings of office and power enshrined in the constitution nobody in the country enjoyed a higher title than Mr.

More than two centuries later the basic tensions highlighted by those deliberations still inform the contradictory characteristics Americans seek in a president. On the one hand they want him (and so far it has always been a him) to be just like them. Frustrating though it may be to those who follow policies and platforms, the polling questions about whom voters would most like to have a beer or carpool with matter. They suggest a human connection, even if it is only imagined, that is neither irrational nor entirely shallow. People want to know that the person they are electing can relate to them and their daily lives. When George Bush Sr announced himself "amazed" at the sight of an electronic scanner in 1992 it helped frame him as out of touch as the nation emerged from recession.

On the other hand there is a desire for the president to exude the gravitas of the office. Indeed, there is a reverence for the post that verges on the indecent in a democracy. So when people refer to "presidential" qualities they are not talking about human attributes but traits that might emerge almost magically from the seal itself. It's as though the occupant of the West Wing must have singularly impressive and uncommon abilities and judgment worthy of heading a nation many refer to as "God's own country".

Needless to say this navigation between the ordinary and the extraordinary is little more than a mediated performance. The fact that George W Bush clears brush, Barack Obama plays basketball or Bill Clinton eats fast food is unremarkable. The fact that they are seen doing it is what is significant. In a controlled media environment what you are allowed to see them doing matters.

Obama performs the presidency badly. Over the past two years he has managed to come across as aloof, detached and occasionally dithering. On a human level his professorial demeanour makes him look like a leader who understands but does not necessarily feel. On a presidential level it makes him look like a leader who prefers to think than to act.

This dislocation is particularly acute because his candidacy – rooted in the promise of change – endowed his presidency with expectations of transformation both symbolic and substantial that no individual could possibly meet.

This became painfully apparent last week during a televised town hall meeting when Velma Hart, a black woman – the demographic bedrock of Obama's base – expressed her frustration with his presidency. "I'm exhausted. I'm exhausted of defending you, defending your administration, defending the mantle of change that I voted for, and deeply disappointed with where we are right now."

Obama acknowledged hard times but went on to answer with a laundry list of achievements. His answer was competent but at no time did it emotionally connect with her or anyone else. Afterwards, Hart told the Washington Post: "I think he has made progress. I just thought by now the progress would be more evident for the man-on-the-street level. I thought there was something special and secret he knew that would make things operate differently."

Asked if she thought her expectations had been unrealistic, she said: "Absolutely. It took decades to get here. He's only been in office for two years. But I guess I started to believe, on some small level, that he had a magic wand."

In the absence of a magic wand Obama's task is to funnel that utopian energy he unleashed into the incremental realities and institutional limits of his office. He campaigned in the big picture; now he must govern in detail. In a practical sense this is not a problem: he is clearly more comfortable in shades of grey than in black or white. For example, in Bob Woodward's new book, Obama's Wars, he says he doesn't think about the Afghan war in "classic" terms of winning or losing: "I think about it more in terms of: do you successfully prosecute a strategy that results in the country being stronger rather than weaker at the end?"

This cerebral trait was once regarded as an asset. Whereas his predecessor was impetuous, Obama was praised for being contemplative and unflappable. Bush had a gut; Obama had a brain. Bush was the "decider"; Obama was the thinker. After eight years of a president who mastered a performance that did not square with reality and had no patience for policy, the country was ready for more substance.

But performatively, it is insufficient. It turns out that there are moments when flappable beats stoic in public perception. His slow-burn approach to problem-solving conveys to many not deliberation but detachment. He has proved, at times, unable or unwilling to reflect the public mood. During the Louisiana oil spill he came off as insufficiently angry and urgent.

Whether one thinks these impressions should matter or not is an entirely different issue to whether they do. Take the economy. Throughout the recession Obama has appeared insufficiently impatient and distraught at the pace of improvement and the toll it is taking on ordinary families. Perceptions of his lack of urgency relate to the slow rate of progress his policies are having on the economy and the fact that most of his signature achievements – the stimulus bill and healthcare reform – have not been experienced by most as having improved their lot.

When he took office 72% of voters believed he understood "the problems of people like you" – that figure is now down to 50%. Many Democrats are desperate for him to feel somebody's pain.

'I would like to see him be a lot less cerebral and a little more emotional," Jim Moran, a Democratic congressman from Virginia, told the New York Times. Others just want him to come across as more accessible. "He needs more Ray's Hell Burgers and less candlelight dinners," said Kenneth Duberstein, Ronald Reagan's former chief of staff (who supported Obama in 2008).

Last week Bill Clinton, the performer- in-chief, gave his advice: "Embrace people's anger, including their disappointment at you," he told politico.com. "And just ask 'em to not let the anger cloud their judgment. Let it concentrate their judgment. And then make your case."

Obama does have a case. But his tepid economic policies mean it's not as good as it might be and his poor performance means he doesn't make it as well as he might do. The next time he meets someone like Hart he not only needs something more impressive to say to her, he needs to find a more impressive way of saying it.