(CNN) -- As political newcomer Alvin Greene calls on South Carolina's Democratic establishment to get behind him, party leaders are calling for an investigation into his surprise win in the state's Democratic Senate primary.
Greene, 32, is an unemployed veteran who came out of nowhere to win last week's election. Despite running no ads, Greene toppled former state legislator Vic Rawl with almost 60 percent of the vote. He'll face Republican Sen. Jim DeMint in the general election.
South Carolina Rep. James Clyburn said Sunday that he has no plans to get behind Greene and repeated his suspicions that the Democratic nominee is "someone's plant."
"I know a Democratic pattern. I know a Republican pattern, and I saw in the Democratic primary elephant dung all over the place," Clyburn, the majority whip, said on CNN's "State of the Union."
Clyburn has called for an investigation into the source of funds that Greene used to pay his state party's $10,440 filing fee. He has also asked the S.C. Democratic Party to request that the federal government investigate the matter, said Kristie Grecko, a spokesperson for his office.
Greene, who paid the filing fee in March, maintains that he funded his campaign entirely with personal money.
Asked Sunday whether he thinks Greene is a legitimate candidate, White House senior adviser David Axelrod said, "it doesn't appear so to me."
"The whole thing is odd. I don't really know how to explain it, and I don't think anybody else does either," he said on NBC's "Meet the Press."
Axelrod said the Democrats of South Carolina deserve a "strong, credible candidate."
"How he won the primary is a big mystery, though, and until you resolve that I don't think he can claim to be a strong, credible candidate," he said.
Greene's primary opponent has also questioned the primary outcome. Rawl said election results experts not affiliated with his campaign analyzed the results and their findings "concern the campaign, and should concern all of South Carolina."
"We do not know that anything was done by anyone to tamper with Tuesday's election, or whether there may have been innocuous machine malfunctions, and we are promoting no theories about either possibility. However, we do feel that further investigation is warranted," Rawl said in a statement.
South Carolina Democratic Party Chair Carol Fowler asked Greene to step down last week, following media reports that he is facing a felony charge.
Public records from the Richland County Fifth Judicial Circuit show that Greene was arrested on November 12, 2009, and charged with "disseminating, procuring or promoting obscenity."
"We are proud to have nominated a Democratic ticket this year that, with the apparent exception of Mr. Greene, reflects South Carolina's values. Our candidates want to give this state a new beginning without the drama and irresponsibility of the past eight years, and the charges against Mr. Greene indicate that he cannot contribute to that new beginning. I hope he will see the wisdom of leaving the race," she said in a statement.
The State newspaper in Columbia, South Carolina, reported that Green was arrested after a University of South Carolina student alleged that Greene showed her pornographic pictures in a computer lab and suggested they go to her room.
Asked by CNN on Saturday about the charges, Green answered, "I have no comment. I want to talk about the issues."
Despite the growing chorus of opposition, Greene has given no indication of plans to drop out.
"I'm on the ballot from here on out. I'm in all the way, and I'm the best candidate for United States Senate in this race in South Carolina," Greene told CNN's Don Lemon in a phone interview Saturday.
Greene, who says his platform focuses on jobs, education and justice, refused to comment on the pending charges against him.
Asked about concerns from lawmakers that he may have mental impairments, Greene responded with a chuckle, "they're the knuckleheads."
In an earlier interview with CNN, Greene described himself as a former member of the armed forces, serving stints in the U.S. Air Force, South Carolina Air National Guard, U.S. Army and the South Carolina Army National Guard. Greene said he was discharged from the Army nine months ago and now lives at home with his father.
He described his discharge from the Army as "involuntary."
He also noted that he would like to see Korea be governed "under a single democracy" similar to how East and West Germany were united after being divided during the Cold War.
Greene said that when he was serving in the Army he was stationed in South Korea from June 2007 until June 2008. But he noted that "my domestic issues are the priority, this is what we have to take care of first."
CNN's Kristi Keck, Mark Preston and Jillian Harding contributed to this report.