Murphy charged that because Scalia and Thomas attended a conference with two Kansas businessmen who benefitted from the Citizens United case, and because this happened while the case was before the court, this is a possible conflict of interest.

"This nation's confidence in the blind justice of the Supreme Court has been badly shaken recently by a series of revelations regarding possible conflicts of interest by Justice Scalia and Justice Thomas in the Citizens United case," Murphy said. Murphy's argument appears to be based on complaints by Common Cause, which has made identical charges.

While conservatives have rejected these arguments, Murphy said the two justices attended the conference, "and they thought it was just fine. They didn't recuse themselves from the Citizens United decision at all."

Murphy said a proposal to require "sunlight" on Supreme Court proceedings is "no undue burden" and urged other members to support his bill when it is introduced.