The Tea Party flexed its muscle to help Republicans gain control of the House of Representatives in 2010, and this year one group hopes to "revolutionize" the vetting process for the next presidential election - starting Wednesday with the first presidential Twitter debate. But four of the GOP field's most visible candidates have declined to participate.

Along with local tea party groups, Arizona-based grassroots organization TheTeaParty.net is holding the debate in Concord, New Hampshire. From remote locations, candidates will tweet their answers to questions 140 characters at a time, limited by a pre-determined time constraint.

Former Speaker of the House Newt Gingrich, businessman Herman Cain, former Sen. Rick Santorum, and former New Mexico Governor Gary Johnson have confirmed their attendance. The group also expects Minnesota Rep. Michele Bachmann and Michigan Rep. Thaddeus McCotter to join.

"We're hoping to revolutionize the debate process in America," says Dustin Stockton, media events director for the group, which provides resources and guidance to local tea party organizations.

"Looking forward to participating in the first ever presidential debate on Twitter today at 3pm," Gingrich tweeted Wednesday morning.

But critics of the social media debate say its scattered attendance is evidence that a debate constrained by character limits and sponsored by a little-known group will have little impact on the race for the White House.

Presumed frontrunner Mitt Romney, Texas Rep. Ron Paul, and former Utah governor Jon Huntsman will not participate. The group originally listed Tim Pawlenty as a participant, but the former Minnesota governor had a scheduling conflict, Stockton says.

The debate has also received little attention from larger, more well-known tea party groups. Stockton says invitations to the Tea Party Patriots and the Tea Party Express went unanswered.

"I'm glad to see candidates participating in something new and unique," Levi Russell, Tea Party Express communications director, told FOX News in an email. "Twitter is obviously a little impersonal and limiting compared to seeing a candidate in person or on live TV, so it will be interesting to see what sort of impact it has." The Tea Party Express is cosponsoring its own televised debate with CNN on September 12 in Tampa, Florida.

Stockton says that conjectures about the limitations of substantive exchanges on Twitter are simply untrue. "We think the exact opposite will be true. Because of the silent medium, we'll get firmer answers," he says. "It takes away from the oratorical skills of the candidates to be evasive and dodge questions."

"A couple really cool things that I think this format will bring out that the traditional or modern debates haven't done: It allows us to ask all the candidates one question at the same time, and see the answers come back at the same time."

Whether tweeted or televised, the Tea Party Express's Russell says that any tea party debate speaks to the influence of the grassroots groups. "The idea of a tea party-hosted debate is very exciting, and is a great demonstration of the continuing influence of this movement."

"These types of events are very important as candidates compete for tea party support, and our expectation is that a clear winner will emerge for the tea parties to start to coalesce behind after 9/12," he predicts.