"Vast Right-Wing Conspiracy" was a phrase used by First Lady Hillary Rodham Clinton in 1998 in defense of her husband President Bill Clinton and his administration during the Lewinsky scandal, characterizing the Lewinsky charges as the latest in a long, organized, collaborative series of charges by Clinton political enemies.

The Today Show interview
Hillary Clinton was referring to the Arkansas Project.

Context
Hillary Clinton's allegations included attacks against independent counsel Kenneth Starr, whom she claimed routinely leaked information damaging to her husband. Starr challenged these allegations in the federal courts, which found no evidence of any such leaks.

Left analysis
David Brock, a conservative-turned-liberal pundit, has said he himself was once a party to an effort to dredge up a scandal against Clinton. In 1993 Brock, then of the American Spectator, was the first to report Paula Jones' claims. As Brock explained in Blinded by the Right, after learning more about the events and conservative payments surrounding Paula Jones he personally apologized to the Clintons. He documented his experience in Blinded by the Right: The Conscience of an Ex-Conservative, wherein he alleged that Arkansas state troopers had taken money in exchange for testimony against Clinton which Brock had published in a previous book. Adam Curtis also discusses the concept in his documentary series The Power of Nightmares. Brock has confirmed Clinton's claim that there was a "Right wing conspiracy" to smear her husband, quibbling only with the characterization of it as "vast", since Brock contends that it was orchestrated mainly by a few powerful people.
Claims have also been made against Republican supporter and billionaire Richard Mellon Scaife, whom former Clinton White House Counsel Lanny Davis once claimed was using his money "to destroy a president of the United States." Scaife claims to be public about his political spending (q.v. [1]). CNN stated in a study the news outlet conducted on Scaife, "If it's a conspiracy, it's a pretty open one."[2]
Hillary Clinton later said in her 2003 autobiography that, "Looking back, I see that I might have phrased my point more artfully, but I stand by the characterization of Starr's investigation [regardless of the truth about Lewinsky]."