Conservative interest groups and Republican lawmakers want Justice Elena Kagan off the health care case. Liberals and Democrats in Congress say it's Justice Clarence Thomas who should sit it out.
Neither justice is budging — the right decision, according to many ethicists and legal experts.
None of the parties in the case has asked the justices to excuse themselves. But underlying the calls on both sides is their belief that the conservative Thomas is a sure vote to strike down President Barack Obama's health care law and that the liberal Kagan is certain to uphold the main domestic achievement of the man who appointed her.
The stakes are high in the court's election-year review of a law aimed at extending coverage to more than 30 million people. Both sides have engaged in broad legal and political maneuvering for the most favorable conditions surrounding the court's consideration of the case.
Taking away just one vote potentially could tip the outcome on the nine-justice court.
Republican lawmakers recently have stepped up their effort against Kagan, complaining that the Justice Department has not fully revealed Kagan's involvement in planning the response to challenges to the law. Kagan was Obama's solicitor general, the administration's top Supreme Court lawyer, until he nominated her to the high court last year.