Just a little more than an hour after some House Democrats recently demanded an inquiry into Supreme Court Justice Clarence Thomas’s ethics, Senate Republicans stepped up the pressure on Justice Elena Kagan to take herself out of the court’s decision on the health-care reform act.

The process repeated itself a few days later. House Judiciary Committee Chairman Lamar Smith (R-Tex.) called for the release of more documents about Kagan’s role as President Obama’s solicitor general; the liberal group People for the American Way came out with another broadside against Thomas.

Accusations about both justices, from the left and the right, show no signs of dissipating now that the Supreme Court has said it will review the constitutionality of Obama’s signature domestic achievement, the Patient Protection and Affordable Care Act of 2010.

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Justices decide for themselves whether they have a conflict serious enough to warrant recusal from a specific case, and neither Kagan nor Thomas appears to be considering sitting out the biggest case of the term.

Federal law requires judges, including those on the Supreme Court, to disqualify themselves when their “impartiality might be reasonably questioned,” as well as for specific reasons such as a financial interest or the involvement of a family member in the litigation.

In addition, it calls for recusal when the judge has served in the government and “participated as counsel, adviser or material witness concerning the proceeding or expressed an opinion concerning the merits of the particular case or controversy.”

The charges against Kagan arise from her work as solicitor general, the government’s top appellate lawyer. If she were still in the job, Kagan would be defending the health-care law at the Supreme Court rather than deciding whether it is constitutional.

Kagan was notified by the White House in March 2010 — just before the law was passed — that she was under consideration to be named to the high court. She said during her confirmation hearings that she played no role in preparing for the inevitable legal challenges that were to come.

“I attended at least one meeting where the existence of the litigation was briefly mentioned, but none where any substantive discussion of the litigation occurred,” Kagan said in a written response to questions from Republicans on the Senate Judici­ary Committee.

She said she had never been asked her opinion about the underlying constitutional and legal issues in the lawsuit or reviewed government documents filed in the case. Similarly, Attorney General Eric H. Holder Jr. said lawyers went out of their way to keep from involving Kagan in the discussions.

But congressional Republicans say e-mails released to conservative groups under public records requests raise questions about the White House’s contention she had been “walled off” from discussions about the health-care act. One e-mail from then-Deputy Solicitor General Neal Katyal says Kagan wanted to make sure her office was involved in strategy decisions, although Katyal said he took the lead and Kagan was not involved.

Another e-mail seemed to indicate enthusiasm for the bill. In response to a message at the time of the vote from Harvard law professor Laurence H. Tribe, then working at the Justice Department, Kagan wrote: “I hear they have the votes, Larry!! Simply amazing.”

Smith, the Judiciary Committee chairman, and Senate Minority Leader Mitch McConnell have pressed Holder for more information, which his department has been reluctant to provide.

Assistant Attorney General Ronald H. Weich said the lawmakers’ requests on an issue that Kagan testified about at her confirmation hearings were “unseemly.” Submitting to Republicans’ requests for more documents and testimony would be equivalent to a congressional probe on “whether a Supreme Court justice should participate in a case pending before the court,” he said.

Holder is scheduled to testify before Smith’s committee Dec. 8.

Asked whether he was questioning whether Kagan told the truth in her testimony, Smith in a statement did not respond directly. He said the Obama administration has a responsibility to respond to requests from Congress to “clarify any confusion or inconsistencies regarding to what extent Solicitor General Kagan may have been involved in discussions regarding health care legislation and litigation.”

Liberal groups say that Thomas’s conflict comes from the political involvement of his wife, Virginia Lamp Thomas, who has been active in conservative causes since before they were married.

Virginia Thomas has worked for former House Republican leader Richard K. Armey and for the conservative Heritage Foundation. In 2009, she created a group called Liberty Central to advance some of the same political causes as tea party activists, including the belief that Congress and the federal government have strayed beyond the limits of the Constitution. She has since left the organization.

Liberal groups and some Democrats have said her outspoken role creates a dilemma for the justice. They have called for investigations into Thomas’s failure to list his wife’s employers for 13 years, as is required on the justices’ financial disclosure documents. Virginia Thomas’s employment was well known; Thomas said the information was “inadvertently omitted.”

Before he resigned from Congress, then-Rep. Anthony Weiner sent Thomas a letter signed by 71 other Democrats urging Thomas to recuse himself, saying there was a “strong conflict between the Thomas household’s financial gain through your spouse’s activities and your role as Associate Justice of the United States Supreme Court.”

Last week, Rep. Louise M. Slaughter (D-N.Y.) took up the cause, asking Chief Justice John G. Roberts Jr. to have the Judicial Conference investigate Thomas’s omissions.

Thomas has received some high-profile support in the argument that his wife’s political activities have nothing to do with his ability to hear the case — from the court’s liberal wing.

Former justice John Paul Stevens said in response to a question at Princeton University that “I wouldn’t think there’s any possibility that any of the activities of Mrs. Thomas have had any impact on the analysis of Judge Thomas.” And Justice Stephen G. Breyer called it a “false issue.”

The calls for recusal have prompted a lively debate among those who study judicial ethics. John Steele, a California lawyer who teaches legal ethics and helps run a blog called Legal Ethics Forum, said the general consensus among those without a partisan interest is that “we don’t have a case for either one of them recusing.”

“At the end of the day, we have to trust them,” he said, meaning that judges must put aside personal interests to reach legal decisions.

None of the calls for recusals have come from the parties involved in the litigation. Florida Attorney General Pam Bondi (R), whose state spearheaded the challenge of the health-care act, is careful when asked about the issue.

“Those questions are up to the individual justices themselves, and all indications are that all nine justices will participate in this case,” she said in a statement.

Researcher Lucy Shackelford contributed to this report.