In an amicus brief filed in December on behalf of 68 members of Congress, the American Center for Law and Justice, which fights for conservative causes in the courts, argued that Mr. Obama’s immigration actions were unconstitutional because officials had “exceeded the bounds of their prosecutorial discretion and abdicated their duty to faithfully execute the law.” In another brief, the group urged the Supreme Court to invalidate the president’s health care tax subsidies, saying they were the “most egregious example of the administration’s make-it-up-as-we-go approach to implementing” the health care law.

Mr. Morrisey is also seeking to convince a federal court that Mr. Obama’s attempts to have the Environmental Protection Agency set standards for carbon emissions amount to illegal double regulation of power plants, which already must comply with rules about mercury and other pollutants.

Senator Charles E. Schumer, Democrat of New York, said he believed the president’s policies would withstand the legal challenges, saying of the administration, “Certainly, they were very, very careful not to go beyond what the law will allow.”

Mr. Schumer added that the Republican definition of an activist judge was flexible. “They decry the courts’ overruling or implementing things they don’t like,” he said, “but are eager to have the courts implement things they like.”

Jay Sekulow, chief counsel at the American Center for Law and Justice, countered that conservatives were turning to judges more frequently because of Mr. Obama’s moves to enact sweeping policy on his own, and because gridlock in Washington had prevented Republican efforts to stop him.

“The courts are the venue, really, to try to keep the presidential authority in check,” Mr. Sekulow said in an interview. “That’s why the conservatives are turning to the courts.”