Much hope has been invested in Barack Obama's ability to strike a new course for the US following eight years of Bush administration unpopularity. Yet many in the US and abroad are impatient with the pace of progress under the Obama administration. The president made the rounds on five news talkshows on Sunday as he pressed his policies and vision, preparing for what is likely to be a difficult week.

Besides the ongoing battle over healthcare, this week sees two showdowns between Europe and the US that will reveal further slippage in American global leadership. The first showdown comes today at a UN special session on climate change in New York City; the second will come at the end of the week at the G20 meeting in Pittsburgh, where America and Europe will butt heads over financial system reforms designed to ensure that the AIGs of the world can never again cause an economic collapse.

Europe has been increasingly critical of America's failures to live up to its global responsibilities. The US is not only the world's largest emitter of greenhouse gases but is by far the largest per capita emitter of carbon and other pollutants. China comes close to the US in terms of total carbon emissions, but it has four times more people, who each belch far less individually. Europe, while having much the same high living standard, has an "ecological footprint" that is only half of America's, since Europe has taken leadership in implementing renewable technologies and conservation practices.

On the campaign trail, Barack Obama promised to reverse the Bush administration's terrible ecological record. Yet so far the world has seen more symbolic gestures from the Obama administration than accomplishments. Its biggest achievement so far has been a disappointment. President Obama signed an executive order to increase US motor vehicle mileage standards – but only to a level that will push fuel efficiency by 2020 to a level that European and Japanese cars reached several years ago, and even China has already achieved.

Europe has announced donations of $2bn to $15bn a year for the next decade to help developing nations cope with climate warming, yet the Obama administration has not offered anything close to that amount. Europe also wants binding, near-term targets for developed nations, proposing a 20% reduction from 1990 levels by 2020, or 30% if everyone agrees. The Bush administration of course rejected such targets – but now it looks like the Obama administration is not willing to go much further. It has said such targets should be voluntary but verifiable.

With the US Senate bogged down in the fight over reforming healthcare, American leaders have said that the senators might not move on climate legislation until 2010, well after the global climate change conference in Copenhagen in December. That drew a sharp response from John Bruton, head of the European Union delegation: "The United States is just one of the 190 countries coming to this conference," Bruton said, "but the United States emits 25% of all the greenhouse gases that the conference is trying to reduce. I submit that asking an international conference to sit around looking out the window for months, while one chamber of the legislature of one country deals with its other business, is simply not a realistic political position."

Even Europe's conservative politicians, such as Connie Hedegaard, Denmark's minister of climate and energy, are expressing impatience: "It's rather crucial that the US can show a credible pathway," Hedegaard said, pointing out that the US emits twice as much carbon dioxide per capita as Denmark, without gaining anything in improving its quality of life.

That's the start of President Obama's week. At the end of it, President Obama will appear at a meeting in Pittsburgh of the G20, a bloc of both developed and developing nations, representing 85% of the world's economic output and most of its population. On the table will be reforms designed to avoid a repetition of the financial panic and global economic collapse perceived as having originated on Wall Street. Despite immense, taxpayer-financed rescue packages needed to overcome the crisis, the financial sector in the US is rapidly returning to business as usual. Indeed, three US banks – Goldman Sachs, Morgan Stanley and JP Morgan – which received some $45bn of bailout aid, each paid billions of dollars more in bonuses in 2009 than they earned in 2008.

Here again, Europe is leading, while the Obama administration is dragging its feet. Europe has proposed far-reaching reforms designed to impose new rules on executive pay and bonuses, requiring that banks link pay to long-term rather than short-term performance, and that they "claw back" any bonuses received in the face of losses. Europe wants a financial police force that has powers to slash payments where investments prove to have failed, and to force boardrooms to control levels of speculation. Europe also wants to block the exercising of stock options for set periods and expose top bank directors to penalties, following huge payouts to failed bank chiefs.

The Obama administration's approach has been much more tepid, to say the least. The US financial industry, as expected, is fighting these reforms, but what do we make of a recent quote by President Obama questioning the need for supporting Europe's proposals. "Why is it," he asked during a recent interview, "that we're going to cap executive compensation for Wall Street bankers but not Silicon Valley entrepreneurs or [American] football players?"

Besides the fact that President Obama was wrong – the National Football League does have salary restrictions – Silicon Valley businesses and NFL quarterbacks don't cause an economic collapse when they screw up. It's very sobering that, if David Letterman read that quote on his TV show and asked his audience: "Who made this clueless statement, former President Bush or President Obama?" we know what the response would be. Or would have been.

In response to American foot-dragging, European leader Jean-Claude Juncker said Europe should act on the bonus issue "whether the Americans are with us or not." He said that a Europe-only charge "will take on such force over time that the Americans will not be able to sit on the sidelines."

Many leaders and supporters are beginning to wonder what is causing this growing gap between the Barack Obama that many people saw on the campaign trail, and the Obama they see in the White House? Beyond Obama's oratorical skills, which excited not only American voters but people all over the world, he is mostly untested as a politician. His previous experience was only a few years in the US Senate and a few years more as a state senator. A sinking feeling is arising among many that President Obama may not be up to the task, that he may not possess the artful skills needed to accomplish even his own goals.

But it must be recognised that it's not just Obama's shortcomings that are causing the problem. The very structure of the American political system is at the heart of these failures. For example, thwarting Obama on a regular basis is an unrepresentative senate where "minority rule" prevails and undermines what a majority of the country may want. With two senators elected per state, regardless of population, California with more than 35 million people has the same number of senators as Wyoming with just half a million residents. This constitutional arrangement greatly favours low population states, many of which tend to be conservative, producing what one political analyst has called "a weighted vote for small-town whites in pickup trucks with gun racks."

In addition, the senate's use of that arcane rule known as the "filibuster" means you need 60 out of 100 votes to stop unlimited debate on a bill and move to a vote. A mere 41 senators, representing as little as 20% of the nation's population, can stymie the other 80%. Given a vastly unrepresentative senate wielding its anti-majoritarian filibuster, it is hardly surprising that minority rule in the senate consistently undermines majority rule, whether on healthcare, financial industry reform, environmental legislation and many other policies.

Pile on to that an uncompetitive, winner-take-all electoral system, marinated in money and special interest influence, and the sclerotic US political scene is deeply troubling. None of these anti-democratic structural features are going away any time soon. Unless Barack Obama is able to demonstrate a better level of political skill than he has shown so far, everyone needs to fasten their seatbelts. The world is about to enter a challenging phase where the US – the undisputed leader of the free world for the past 60 years – is going to rapidly cede its place at the head of the line.

It appears that the wheels may be coming off the world's post-war leader, and not even Barack Obama can stop it happening.