Washington (CNN) -- Call them "unicorners." A liberal group says it has collected more than 19,000 e-mails requesting Arizona officials to confirm Mitt Romney is not a unicorn.
Without such proof, the group Left Action argues with tongue in cheek, Romney may indeed be a unicorn -- his dark mane hiding a horn -- and therefore ineligible to be on the presidential ballot in November.
The farcical campaign mimics efforts by "birthers," and some top supporters of certain Republican presidential nominee Mitt Romney, to continually raise the already-settled issue of whether President Barack Obama meets the Constitution's requirements for citizenship.
"I feel like we've tried logic with the birthers for too long," Left Action founder John Hlinko said Wednesday. "Now it's time to take their arguments to the logical extreme to show how absurd they are."
While steeped in satire, the unicorn-birther matter touches on deeper issues as Obama and Romney head into the November campaign.
Since before Obama's election in 2008, some conservatives have questioned whether he was born in the United States. If not, they said, he was ineligible to serve as president.
Despite conclusive evidence to the contrary, the issue has remained alive, nurtured by the conservative blogosphere and getting raised repeatedly by Republican figures.
Donald Trump, whose 2011 crusade to unearth details about Obama's origins drew global attention and prompted the White House to release the president's long-form birth certificate, raised the issue again last week.
Before campaigning with Romney on Tuesday, Trump bristled when told by CNN's Wolf Blitzer that he was beginning to sound "a little ridiculous" for characterizing the question of where Obama was born as a matter of opinion, rather than fact.
"You are, Wolf," Trump fired back. "Let me tell you something, I think you sound ridiculous."
The Romney campaign appears anxious to distance itself from the birther issue. When asked Monday about Trump's raising it, Romney said he believes Obama was born in the United States.
"You know, I don't agree with all the people who support me, and my guess is, they don't all agree with everything I believe in," Romney said. "But I need to get 50.1% or more, and I'm appreciative to have the help of a lot of good people."
Obama's campaign jumped on that comment, with deputy manager Stephanie Cutter issuing a statement Tuesday that said Romney's "continued embrace of Donald Trump and refusal to condemn his disgraceful conspiracy theories demonstrates his complete lack of moral leadership."
Meanwhile, the Romney campaign accused Obama supporters of using the issue to distract attention from the high unemployment rate. Romney surrogate John Sununu, a former New Hampshire governor, went further Wednesday, accusing CNN of deliberately focusing on the birther issue in support of Obama.
"Why is CNN so fixated on this? Why don't we talk about the jobs issue in this country?" Sununu asked after CNN's Soledad O'Brien raised the birther issue to start an interview. "It's CNN that wants to bring it up. I don't want to bring it up. Mitt Romney made it clear that he believes that President Obama was born in the United States."
When O'Brien responded that Trump's raising of the birther issue made it a valid question about a possible major contributor to the Romney campaign, Sununu fired back that comedian Bill Maher -- known for politically incorrect commentary -- is a Democratic supporter.
"The fact is that this country has a jobs problem, and supporters of the president like CNN keep wanting to talk about other issues," Sununu said.
Pressed on the matter by O'Brien, Sununu declared, "It's not an issue. There is nobody in the Romney campaign that believes that the president was not born in the United States. Donald Trump is wrong. The president is born in the United States."
Hlinko of Left Action called Sununu's pronouncement "a good start," but he called on Romney and other Republican leaders to make that point directly to birthers to halt what he labeled a racism-tinged attempt to delegitimize the nation's first African-American president.
"It is the Republican grass roots and Republican leaders who keep on raising it," Hlinko said of the birther issue, adding that Romney and other GOP leaders "refuse to actively push back."
"They're not just saying, 'This is nonsense, and it's tinged with racism, and it needs to stop,' " Hlinko said.
While targeted at Romney, the unicorn campaign actually is satirizing last week's justification by Arizona Secretary of State Ken Bennett for threatening to bar Obama from the November presidential ballot.
Bennett, who initially said his office received 1,200 e-mails from Arizonians questioning whether Obama was born in Hawaii, said that he was duty-bound to investigate that public concern.
It didn't matter that the White House last year released Obama's long-form birth certificate from Hawaii. Trump and others question whether the document is authentic, and Sheriff Joe Arpaio of Arizona's Maricopa County -- known for his tough crackdown on illegal immigrants -- has sent a deputy to Hawaii to check it out.
Bennett, a co-chairman of Romney's Arizona campaign, defended the request for proof from Hawaii, telling Arizona radio station KTAR last week that "I don't see anything wrong with verifying something so that as many Arizonans as possible have confidence that the people that appear on the ballot are entitled to be there."
"If I embarrassed the state, I apologize," he said.
When Hawaii later provided the requested proof, Bennett announced the matter settled and said Obama would be on the ballot in Arizona as long as he filed all the proper paperwork.
Hlinko called the episode "asinine," saying it was the "straw that broke the camel's back" for inspiring him to launch the Romney-unicorn campaign.
He created a website labeled www.MittRomneyisAUnicorn.com and spread the word using his network's Internet connections on Facebook and other sites.
"What about the persistent rumors that Mitt Romney is in fact, a unicorn?" the website says, using italics for emphasis. "There has never been a conclusive DNA test proving that Mitt Romney is not a unicorn. We have never seen him without his hair -- hair that could be covering up a horn."
Lampooning the logic of birthers, the website says: "No, we cannot prove it. But we cannot prove that it is not the case. And if Mitt Romney is or may be a unicorn, he is not constitutionally qualified to be president."
On Wednesday, the website said it had more than 19,000 e-mails supporting an investigation by Bennett into Romney's possible unicorn heritage.
Birther theories vary. Some argue Obama was born in Kenya, not Hawaii, and therefore cannot serve as president. Others focus on the fact that Obama's father was not a U.S. citizen, supposedly rendering his son ineligible for the Oval Office.
Earlier this month, the Iowa state GOP wrote a passage into its proposed party platform calling on presidential candidates to "show proof of being a natural-born citizen," beginning with the 2012 election.
"There are many Republicans who feel that Barack Obama is not a 'natural-born citizen' because his father was not an American when he was born and, therefore, feel that according to the Constitution he's not qualified to be president, should not have been allowed to be elected by the Electoral College or even nominated by the Democratic Party in 2008," Don Racheter, chairman of the Iowa Republican Party's platform committee, told Radio Iowa.
In addition, Republican Congress members from Florida, Colorado and Missouri have publicly raised questions about Obama's citizenship in recent weeks.
Republican National Committee Chairman Reince Priebus calls the birther issue a distraction, and Sununu sought to turn the tables on the matter Wednesday by arguing it was the Obama campaign seeking to use the topic to distract.
"I think it's an effort by the Obama administration not to talk about the laws they passed that are strangling specific segments of the American job market," Sununu said.
To Hlinko, Sununu "knows in his heart" that the birther discussion "is a losing issue."
CNN's Peter Hamby contributed to this report.