Her critics point to a 2010 case regarding a San Francisco health measure, in which then-Solicitor General Kagan's office filed an amicus brief touting the newly passed health care law.
In May 2010, after Kagan had been nominated to the nation's highest court, Principal Deputy Solicitor General Neal Katyal sent her a memo outlining the cases in which she had "substantially participated." Kaytal specifically referenced the Golden Gate case, noting that it had been "discussed with Elena several times."
That's enough to convince Heritage Foundation Senior Legal Fellow Hans von Spakovsky that Kagan shouldn't take part in the current health care case before the high court.
"I don't see how any ethical lawyer adhering to professional codes of conduct could not consider that they need to recuse themselves from this case," he said.
Earlier this week, the Supreme Court denied a motion by the group Freedom Watch, which has called for Kagan's recusal. Freedom Watch's motion asked for permission to take part in the oral arguments scheduled for March 26 to 28. That motion was denied, and Kagan took no part in its consideration.
Other legal scholars say Kagan is in the clear, noting that the issues in the Golden Gate case are distinct from those in the case now pending at the Supreme Court.
"Absolutely different cases, absolutely two different sets of issues, and it does not in any way support the idea that Justice Kagan should recuse herself," Elizabeth Wydra, chief counsel at the Constitutional Accountability Center said.
Wydra says repeated attempts by Freedom Watch could hurt their credibility with the court, adding, "The arguments are, frankly, looking a little desperate."
Kagan isn't the only justice under scrutiny. A number of Democratic lawmakers have also called for Justice Clarence Thomas to take himself off the case. They say his wife's work for a group looking to repeal the health care law creates a conflict of interest.
Chief Justice John Roberts, clearly aware of recusal calls by outside groups, addressed the issue in his yearend report issued in December. In it, Roberts stated that he has "complete confidence" in the capability of his colleagues to make their own decisions.
Shannon Bream joined Fox News Channel (FNC) in 2007 and is a Washington-based correspondent covering the Supreme Court. She also serves as the anchor of "America's News Headquarters" (Sundays at 12-2PM/ET). Click here for more information on Shannon Bream.