If 5,000 people sign, Adam Green, the veteran online political activist at the head of the coalition of left-of-center groups, economists and bloggers behind the petition, says they'll deliver it to CNBC headquarters. "That would likely be something of a media spectacle," he said, hopeful the stunt might embarrass the network into changing.

Last evening, the group was more than halfway to its goal.

Stewart has repeatedly pounded CNBC over the past couple of weeks for being too cozy with corporate executives and urging investors to buy stocks even as the market lost much of its value over the past year and a half, culminating in his much-discussed interview with Mad Money host -- and BloggingStocks contributor -- Jim Cramer last week.

"He made the intellectual case for why CNBC needs to hold Wall Street accountable," Green says. "But no one was engaging in activism around that to make sure CNBC changes its ways."

Stewart's main point, according to Green: "Things will continue to be wrong at CNBC if they don't change their entire way of operating in which they favor access to Wall Street so much that they aren't willing to challenge."

In addition to challenging Wall Street CEOs more aggressively in interviews, the petition also asks CNBC to diversify its stable of analysts and "hire some new economic voices."

Atop their list: Dean Baker, the co-director of the Center for Economic Policy Research, a Washington think tank. Baker wrote a report in 2002 entitled "The Run-Up in Home Prices: Is It Real or Is It Another Bubble," predicting a fall in home values that could lead to economic calamity.

"We're sitting here in the worst economic downturn since the Great Depression and, for me at least, the warning signs were everywhere," Baker says. "And for the most part you didn't get them from CNBC." Baker is also one of about 30 economists, liberal journalists, activists and media watchdogs to sign the letter.

An after-hours message for CNBC's public relations team wasn't immediately returned.

If Green and his crew are successful in harnessing the Daily Show host's rants to affect change at CNBC, it wouldn't be the first time Stewart got credit for changing a network's approach to the topics it covers. Stewart's incendiary 2004 appearance on the CNN political debate show Crossfire -- in which he accused the program's panelists of participating in "partisan hackery" -- is often cited as one of the reasons it was eventually canceled.