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States had to declare whether they intended to set up state-run exchanges in early December, while states that partner with the federal government in a hybrid exchange must apply by Feb. 15. So far, 17 states and the District of Columbia have obtained conditional approval for in-house exchanges, including several Republican-governed Western states.

Yet 25 states have indicated that they want a federally run exchange, according to the latest data from the Henry J. Kaiser Family Foundation, which has closely tracked the process.

Court papers in the Oklahoma case show a group of business owners attempting to intervene in the case in support of Oklahoma’s position, arguing that the IRS rule will subject them to the health care law’s employer mandate “under circumstances not authorized by law.”

So far, the federal government’s motions to dismiss the case have focused on whether Oklahoma and the intervening business have the proper standing and jurisdiction to bring their lawsuit. In other defenses of the IRS rule, the Treasury has pointed a section of the health care law that requires federally run exchanges to report data about health plan enrollments.

“There would be no reason for Congress to impose this obligation unless the enrolling individuals were eligible for the premium tax credit,” Emily S. McMahon, acting assistant secretary for tax policy, wrote in a letter to Sen. Orrin G. Hatch, Utah Republican, when the topic stirred controversy last year.

The department has argued that opponents of Mr. Obama’s law are attempting to deny billions of dollars in tax credits to middle-class families.

In a November op-ed, Mississippi’s insurance commissioner said the attempt to poke holes in the IRS rule-making is “flawed in that it is based solely on speculation and unproven legal theories.”

But those critical of the IRS say the administration figured that conservative-led states would jump at the chance to run their own affairs instead of letting the feds step in. The tax credit for state-run exchanges was an intentional move aimed at compelling governors to set up their own exchanges, Mr. Cannon said.

“They meant to do this,” he said.

Republican House members say they are trying to enforce the law as it was written and will sharpen their examination of IRS decision-making in the coming year.

In a December letter, Mr. Issa and two Republican colleagues — House Ways and Means Committee Chairman Dave Camp of Michigan, and Rep. Charles Boustany Jr. of Louisiana — asked Treasury Secretary Timothy F. Geithner to turn over unredacted documents related to the decision to extend the tax credits “despite having no authority to do so under ObamaCare.”