Updated

Ted Olson's confirmation to be the Solicitor General of the United States — the person responsible for arguing government cases before the Supreme Court — is facing significant complications, according to a Democratic source on Capitol Hill.

The scrutiny is over Olson's alleged past involvement in the American Spectator magazine's so-called "Arkansas Project." The project was a long running investigation of Bill and Hillary Clinton and funding for the magazine's investigative efforts came from conservative philanthropist and newspaper publisher Richard Melon Scaife

The source ultimately believes Olson will be confirmed if and when this matter is "cleared up."

The source says that Olson, who represented George W. Bush before the Supreme Court in the wake of the Florida election standoff, has been "under-telling" the truth about his involvement in that project. Capitol Hill Democrats are looking into questions of whether or not Olson perjured himself during his confirmation hearing when answering questions about the project.

During questioning, Olson said, "It has been alleged that I was somehow involved in that so-called project. I was not involved in the project, in its origin or its management."

In subsequent letters to Democratic Sen. Patrick Leahy, Olson insisted he "became aware of the 'Arkansas Project' at some point in 1997."

But that statement is in conflict with comments made by former American Spectator reporter David Brock who claimed to be at dinners where Olson participated in "brainstorming sessions" for the project.

There is, however, also a question about whether Brock has an axe to grind in all this. After Brock softened his political orientation as a conservative attack-dog scribe and published a rather flattering book about Hillary Rodham Clinton, Olson's wife, Barbara, withdrew a party invitation she'd earlier sent to Brock.

The snub was the topic of much discussion in Washington at the time, and the Olsons were asked in 1998 if they had ever talked to Brock about it.

Barbara Olson said, "I've seen him at some different events. I've said hello. He smiles at me and we usually aren't standing near each other afterwards." Speaking of Brock, Ted Olson added that "it's maybe a sign that some people in Washington take themselves way too seriously."

There have now been three rounds of correspondence between the office of Sen. Leahy and Olson on this matter. Leahy is the ranking Democrat on the Senate Judiciary Committee.

Responding to requests for comment, Olson gave Fox News the following statement:

"Everything I told the Judiciary Committee about the so-called 'Arkansas Project' is true. I was not involved in the planning, origination or implementation of the project.

"Of course, I knew just as the public knew, that the American Spectator was working on stories about the Clintons — just like the Washington Post and the New York Times.

"I did not know until relatively late in the game there was special funding for investigative journalism activities at the American Spectator."

The Olson confirmation vote is now on hold for a week. When asked if his confirmation was in trouble, Sen. Leahy said, "I don't make any prediction on that." But privately, Democratic sources on the committee suggest this matter can probably be resolved.