Chip Somodevilla / Getty Images

ABC News’ Ariane de Vogue reports:

Now that the Supreme Court has taken up a challenge to the health care law, advocacy groups on both sides of the ideological spectrum are hoping to get a justice –with potentially opposing views– dismissed from hearing the challenge.

The focus for now from conservative groups is Justice Elena Kagan, while left-leaning groups turn their attention to Justice Clarence Thomas.

The absence of one justice on a close case could change the ultimate outcome.

But at this point the possibility of either Thomas or Kagan stepping off the case, with the information that is publicly available, is remote. Recusal issues are largely left up to the individual Justice and if one had decided not to participate in the closed door deliberations regarding the case it would have been reflected in the order list released from the court last Monday.

“It’s pretty clear they have both decided to sit,” said Monroe Freedman, a Professor at Hofstra Law School.

Carrie Severino, a former clerk of Justice Thomas and the chief counsel of the conservative group Judicial Crisis Network called for the recusal of Kagan citing her previous job as Solicitor General of the Obama administration. Severino said Kagan’s office was “responsible for formulating the administration’s defense” of the health care law.

“To use a sports analogy, would anyone trust the outcome of a close game where the referee had been a coach for one of the teams earlier in the game?” asked Severino in a statement.

During her confirmation hearings for the Court, Kagan told Congress she had never offered any views or comment regarding the merits of a challenge to the health care law brought by lawyers for Florida and several other States who believe the law is unconstitutional. She recalled attending “at least one meeting when the existence of the health care litigation was briefly mentioned,” but she added, “none where any substantive discussion of the litigation occurred.”

Kagan also set out her policy for recusal: ” I would recuse myself from any case in which I played a substantial role” she told senators in her written testimony. “This category would include cases in which I approved or denied a recommendation for action in the lower courts and cases in which I reviewed a draft pleading or participated in formulating the government’s litigating position.”

Another advocacy group, Judicial Watch has released a series of e-mails it obtained from the Department of Justice through litigation between Kagan while she was the Solicitor General and some of her colleagues at the Department of Justice. The emails reflect that she kept up with the health care debate in general terms, and that she was aware that questions regarding her recusal from health care litigation needed to be coordinated.

In a statement the Department of Justice said the documents do nothing to contradict Kagan’s congressional testimony.

“During her tenure, former Solicitor General Elena Kagan did not play any substantive role in litigation challenging health care reform legislation, and the documents that have been released reflect that,” according to the statement.

Tom Fitton, the president of Judicial Watch has not called for Kagan to be recused from the case but he said the emails show a “greater involvement by the Solicitor General’s office in Obama care legislation than had been understood at the time of her confirmation. ”

In one she told her then-colleague Larry Tribe on March 21, 2010– the day the House of Representatives passed the Affordable Care Act–, “I hear they have the votes Larry!! Simply amazing.”

Kagan was responding to an email from Tribe with the subject line of “fingers and toes crossed today.”

Freedman said that even if one takes the email not as a statement of fact, but an approval of legislation, “that is not enough to justify her recusal.” “She did not express any opinion on the constitutionality of the statute,” he said. “In addition she and others have denied that she participated in any way in any litigation or strategy sessions. If she did , there is no question she must recuse herself.”

The emails reflect that Kagan was aware that the issue would draw interest from the press in the early days after her nomination to the Court. Seven days after the announcement of her nomination , Tracy Schmaler a press officer at the Department of Justice, emailed Neal Katyal, who was then Kagan’s top deputy. Schmaler asked if Kagan had been involved in the preparations for health care litigation. Katyal emailed back a minute later.

“No she never has been involved in any of it. I’ve run it for the Office, and have never discussed the issues with her one bit.”

Katyal then forwarded the email to Kagan, adding, “This is what I told Tracy about health care.” Kagan responded to both Katyal and Schmaler.

“This needs to be coordinated. Tracy, you should not say anything about this before talking to me.”

On Tuesday night Senator Jeff Sessions (R-Alabama) a senior member of the Senate Judiciary Committee sent a letter to Attorney General Eric Holder saying that he was “deeply disturbed” that the emails hadn’t been provided to the Senate Judiciary Committee during Kagan’s confirmation hearing.

Although Holder has recently testified that Kagan was “physically, literally ” moved out of the room “whenever a conversation came up about health care freeform legislation”, Sessions asked for more details on her role.

Stephen Gillers, a professor of law at New York University School of Law who is an expert on legal ethics, thinks the emails do not reflect that Kagan should recuse herself. But he is sympathetic to Sessions request for the documents.

“It makes the Department of Justice look bad to wait so long and to release them episodically.. It creates suspicion.” he said.

While conservative groups have suggested a conflict for Kagan, liberal groups and some Democratic congressmen see the same for Justice Clarence Thomas.

Last February 74 congressmen lead by the now-disgraced Rep. Anthony Weiner, D-NY, wrote Thomas a letter asking him to recuse himself from hearing cases on the health care reform law because of his wife’s ties to a group opposing the health care law. The liberal group People for the American Way posted a letter on its website arguing “Justice Thomas’ wife Ginni has earned hundreds of thousands of dollars working for and leading groups that have repealing health care reform as one of their chief goals. Considering challenges to the health care law are expected to reach the Supreme Court, that could present a major conflict of interest.”

Gillers –who points out that Ginni Thomas was involved in conservative causes long before she met her husband– does not believe that Thomas has any reason to recuse himself either. “I don’t think there is any basis for Thomas to recuse. My view is judge or a justice is not burdened by the political activity of a spouse., ” he said. “Ginni Thomas has a first amendment right to proclaim her views as vociferously as she wants. We have to trust Justice Thomas to come to his own conclusions.”

Freedman thinks the Thomas case is a closer call.

“Thomas should recuse himself because his wife is a lobbyist for groups that are opposed to the health care law. She has brought in a lot of money in family income opposing the health care law, ” he said. “Thomas has a financial family interest in the success of the opposition to health care. ”

Supreme Court Justices are governed by two sets of ethics rules.

A federal statute, applicable to Supreme Court , says that a judge should “disqualify” himself [or herself] in any proceeding in which his impartiality might reasonably be questioned. Also, the Judicial Code of Conduct –a set of ethical principles adopted by the Judicial Conference – uses a similar standard.

But the Code of Conduct is only applicable to lower court judges, although Supreme Court justices often follow the guidelines. Some believe the Code should apply to the Supreme Court as well.

Justices Stephen Breyer and Anthony Kennedy spoke about the issue last April in front of the House Appropriations Subcommittee in a hearing to review the court’s budget.

Kennedy said he did not feel the code should be binding.

“There’s a legal or constitutional dissonance or problem,” he said, noting that the rules are made by district and appellate court justices. “We would find it structurally unprecedented for district or appellate court judges to make rules that the Supreme Court would follow.”

Breyer said the rules should be diffferent at the Supreme Court level because the court itself is different.

“We do follow the rules and they do apply,” but he added that, unlike in the lower courts, if a Supreme Court justice recuses himself from a case his vote cannot be replaced. “It’s a different thing … being a Supreme Court justice,” he said.

“You have a duty to sit because there is no one to replace me if I take myself out, and that could sometimes change the result.” Kennedy added that if the court deadlocks 4-4 on an issue, the lower court ruling stands. “If we have one of us recused from a case and we come out 4-4,” he said, “we’ve wasted everyone’s time.”