To some Americans he is the most trusted man in the US since the iconic news anchor, Walter Cronkite, told the country that the Vietnam war was a lost cause.

Yet Jon Stewart, the presenter of the satirical Daily Show who calls the president "dude" to his face and gets away with it, is about to put that credibility on the line with his "rally to restore sanity" in Washington tomorrow.

The comedian, who was recently voted the most influential man in America by a men's magazine, has promised nothing more than "fun" for the tens of thousands he hopes to draw to the National Mall in Washington DC. The fun will include singers such as Sheryl Crow and readings by well-known actors.

But the timing – days before the midterm elections that promise a conservative resurgence – and Stewart's overtly liberal views have some on the left hoping that he can magically inject their cause with the enthusiasm that has been severely lacking in the campaign.

Others are taking the rally at face value and planning to turn up with banners proclaiming themselves part of the reasonable majority, liberal or conservative, against the particular brand of insanity that has swept America since Barack Obama entered the White House.

The president's more extreme but very vocal critics portray him as a communist for promoting universal access to healthcare or Hitler for allegedly planning to impose what Sarah Palin called "death panels" on hospitals. Movements have been built around claims that the president was born in Kenya or is a secret Muslim.

Then there is the Daily Show's battle with Glenn Beck and Fox News and their ceaseless peddling of conspiracy theories involving Obama and the Democrats. It was Beck's own right-wing "rally to restore honour" in August that prompted Stewart's call to fill the mall tomorrow.

Some Democrats hope that the rally will help fire up the supporters who turned out in large numbers to vote for Obama two years ago but who now appear disillusioned.

Stewart says he is merely seeking to reverse the extreme polarisation of politics. Some of his supporters are planning to turn out with banners proclaiming: "Stop it. You are scaring the kids!!", "Be Civil America" and "Team Sanity: I respectfully disagree with just about everything you said".

But the Daily Show presenter, a self-described socialist, is in an unusual position that reflects not only the rapid decline in confidence in traditional sources of news but the inexorable rise of the influence of celebrity in politics, seen when his protege, Stephen Colbert, testified in character as a parody of a rightwing Fox News presenter to Congress last month. Colbert will be at the rally today, leading his satirical "march to keep fear alive".

Where America once looked to Cronkite, it now looks to Stewart precisely because he is not in the traditional news business. Many watch his show not only for a take on the news but for news coverage itself. The Daily Show has twice won the Peabody award for coverage of presidential elections and been nominated for others.

Stewart's credibility is such that the president chose the Daily Show this week for his principal interview ahead of the mid-term elections. It was praised by both Obama's spokesman, Robert Gibbs, and George W Bush's former strategist, Karl Rove.

"Jon Stewart is about as good an interviewer as there is in the public domain right now," Gibbs said.

That has some of his fans worried that Stewart is now, like the reporters he derides, too close to the centre of power. They fear his credibility might be eroding although a similar concern was raised that the Daily Show might lose its bite when Obama was elected and Stewart no longer had such a juicy target in George Bush.

To others, Stewart contributed to the cynicism with the tone of his daily exposure of the failings, lies and hypocrisies of American politicians that can sound awfully like the right's call to fix "broken Washington".

Critics have also emerged from the Washington establishment to question Stewart's audacity in daring to hold the rally at all. Anne Applebaum wrote a critical article in the Washington Post: "Jon Stewart's march is no laughing matter." Her colleague Paul Farhi asked: "Just who does Jon Stewart think he is?"

Yet these are precisely the people who draw Stewart's anger. He has said his show is only necessary because journalists have abandoned their responsibilities through a mix of indifference and a lack of gumption that leaves viewers and readers with no real idea of what is going on.

The eye opener for Stewart came as the Daily Show followed George W Bush's 2000 presidential election campaign.

"The more we got to meet people [in the media], it was 'Oh! You're fucking retarded! You don't care!' The pettiness of it, the strange lack of passion for any kind of moral or editorial authority, always struck me as weird. We felt like, we're serious people doing an unserious thing, and they're unserious people doing a very serious thing," Stewart told New York Magazine last month.

Some American journalists implicitly admit the charge. Brian Williams, the anchor of the NBC nightly news, told the magazine that Stewart "has chronicled the death of shame in politics and journalism".

But the real question of the moment is whether Stewart is going to make any difference to Tuesday's vote. Larry Sabato, a University of Virginia political science professor, thinks not.

"It may cause a few young people to get out to vote but I don't think it's going to cause millions of people to suddenly show up at the polls. In fact, I've had Democrats tell me they're worried some of their volunteer labour that they want to be working in the districts will be going to Washington for the fun," he said.

But fun, after all, is all that Stewart is promising.