The clandestine nature of the session underscores the intense conflict over the spending, which is the subject of a federal lawsuit in which House Republicans have so far prevailed, as well as a continuing investigation by the Ways and Means and the Energy and Commerce Committees. It also shows that more than six years after President Obama signed the Affordable Care Act into law, Republican opposition has not waned.

After failing to win congressional approval for the funds, the Obama administration spent the money anyway and has now distributed about $7 billion to insurance companies to offset out-of-pocket costs for eligible consumers. The administration asserts that the health care legislation provided permanent, continuing authority to do so, and that no further appropriation was necessary.

Mr. Fisher, for one, did not agree, and his testimony is the first to reveal that some within the administration challenged the spending. Beginning in late 2013, he and his supervisor began having qualms about how the White House was planning to proceed. In combing through documents to make sure his agency could defend the spending in future audits, Mr. Fisher said he came up empty.

“Cost-sharing reduction payments are not linked to the Internal Revenue Code, as far as I could tell, directly anywhere,” Mr. Fisher, now in the private sector, said in his deposition, made public last week by House Democrats who feared Republicans would release selected excerpts. “There is no linkage to the permanent appropriation, nor is there any link to any other appropriation that was indicating what account these funds should be paid from.”

Committee Republicans say Mr. Fisher’s sworn testimony, compelled by a rare Ways and Means Committee subpoena, affirms what they thought all along: that the Obama administration knew it did not have the authority to spend the money and did so regardless to strengthen the health care law in defiance of the Constitution. They say the administration violated a fundamental principle of American government: Congress must appropriate any money spent by the executive branch.