Even in the increasingly wild world of American politics, it seemed an especially crazy idea: Matt Damon for president? After all, the handsome actor, whose boyish good looks belie the fact that he has just turned 40, is still best known for his early role in Good Will Hunting, where he played a working-class Bostonian.

Since then, he has won plaudits in Hollywood for solid work in films ranging from action flicks to Invictus, which told the story of post-apartheid South Africa's rugby World Cup triumph.

So why is Damon's name being mentioned in the context of the 2012 race for the White House and a possible liberal challenge to Barack Obama? The simple answer is to blame leftwing firebrand Michael Moore.

Moore, in a discussion with the liberal politics blog Firedoglake, raised the issue as he talked about his frustration with Obama, who many American leftists see as ignoring them while compromising with the Republican party. Moore called Damon's political stances in recent years courageous and urged him to run, despite there being no hint from the actor himself that he would care to. In a nod to the acting past of two-time Republican President Ronald Reagan, Moore said: "The Republicans have certainly shown the way that when you run someone who is popular, you win. Sometimes even when you run an actor, you win."

The suggestion quickly spread across the media, generating a lot of chuckles as well as predictable outrage from conservative pundits. But the suggestion showed two things that are not so easily dismissed. First, quietly and with impressive charm, Damon has emerged as an eloquent and fierce spokesman for a slice of liberal America. On everything from the Iraq war to education policy, he has been happy to take a stand and, rather than praise the president, he has come out publicly to say Obama has "mishandled his mandate".

Second, it showed that America, more than any country in the world, has a fluid boundary between the worlds of entertainment and politics.

From Reagan to Clint Eastwood, Sonny Bono to Arnold Schwarzenegger and Al Franken and many more, the list of US actors and performers turned politicians is lengthy and even distinguished. "The kind of character that pursues an acting career in America is often the same kind of character that pursues a political career. You have to stand up and make people like you and be good on TV," said Professor Robert Thompson, a popular culture expert at Syracuse University. So, Matt Damon for president? In 2012, almost certainly not. But one day? You never know.

Damon is certainly no shallow celebrity, long on good looks but short on brains. The Massachusetts native may have chosen Hollywood as a career, but he is not an actor picking causes with carefully staged press conferences on subjects that no one could dislike, such as stopping African famine.

Instead, Damon has lent his high profile name to the distinctly unfashionable cause of the Working Families Party. The WFP is an obscure leftwing political party that exists as a sort of pressure group in New York state on Democrats and leftists in order to pursue progressive ideals. Attaching your name to the WFP is about as far from trendy as any Hollywood celebrity could get. Yet Damon has been a passionate advocate for the party, appearing in a 2010 campaign video for them in which he urged New Yorkers to shun the Democrats and vote for the WFP as a genuine leftwing alternative.

Damon has won the hearts of many liberals by criticising Obama over policy issues, and standing up for teachers. Speaking at a recent Save Our Schools march in Washington, DC, he angrily denied a reporter's suggestion that teachers were cosseted. "A teacher wants to teach. I mean, why else would you take a shitty salary, and really long hours, and do that job, unless you really love to do it?" he fumed. A video of the encounter went viral, with Damon being hailed a hero by teachers' groups.

Damon, like Sean Penn with Haiti and George Clooney with Darfur, is one of the few big names who can genuinely say they are activists, not just celebrity brands attached to a good cause. He founded the H2O Africa Foundation, which later became Water.org and which aims to bring clean water to disadvantaged people. He has been involved with Darfur. "Matt Damon seems like a real person on these things. He's running that whole water issue. That actually takes up a lot of his time," said Richard Laermer, a celebrity expert and author of the book 2011: Trendspotting. On a host of issues Damon has eloquently and publicly spoken on subjects dear to liberal hearts. He has slammed the recent debt-ceiling deal struck by Obama and the Republicans and called for rich people like himself to be taxed more. He has spoken against the Iraq war.

Perhaps one should not be surprised; Damon is highly educated. Though he eventually dropped out to pursue an acting career, he went to Harvard, where he studied English. His mother – who introduced him at the teachers' rally – is an education professor.

But, experts say, Hollywood has given him what is needed most: name recognition. "An actor has a precious thing in politics. People know who they are and they will pay attention when someone puts a microphone in front of them," said Syracuse's Thompson.

Indeed, that power can make a political career out of the unlikeliest of raw material. Look at how former pro wrestler Jesse Ventura became governor of Minnesota, or how comedian Franken became a senator from the same state and – perhaps most bizarre of all – how Schwarzenegger went from playing a killer robot from the future to being governor of California and responsible for one of the biggest economies on Earth.

The road between Hollywood and politics has also produced notable successes. Franken, a former stalwart of Saturday Night Live, has won plaudits for his seriousness as a politician. Schwarzenegger was seen as a joke when first elected, but he easily won a second term and became known for cutting-edge environmental policies. Most successful was Reagan, who went from a B-movie actor to being one of the most influential Republican presidents of the 20th century. Indeed, while most stars who dabble in public life are seen as "Hollywood liberals", some of the most successful, such as Reagan and Schwarzenegger, have been conservatives.

But the road to political power is not always easy for an actor. On the liberal side of the aisle, Warren Beatty was mentioned as someone who might run for president but never did. And among Republicans, the name of Fred Thompson stands as a salutary lesson in the limits of power. Few people have blurred the lines between acting and politics as much as Thompson, who combined his acting career with becoming a senator from Tennessee. He has played a US president on TV but when he ran for the Republican nomination in real life in 2008, his attempt was a disaster.

So, while Americans are tolerant of actors who want to be politicians, they do not write them a blank cheque. "Celebrity can be a blessing or a curse. You are able to get people to listen to you, but you need to have something they want to hear," said Robert Thompson.