Members of Congress and Capitol Hill staff will be required to pay thousands of dollars more every year for their healthcare unless the glitch is fixed.
Coburn made his announcement at a gathering of the Homeland Security and Governmental Affairs Committee, where lawmakers voted to approve Archuleta by a vote of 7-4.
"There is no reason we should vote on this position until we know what the administration's position is on our employees' health insurance starting Oct. 1," Coburn said.
"I plan on holding that nomination until we get an answer so we can legislate or do something for the very valuable staff that we have and the stupidity for which we have, in the present law, a gutting of our own staff because someone was trying to make a political point."
Sen. Charles Grassley (R-Iowa), an opponent of healthcare reform, was the original proponent of putting lawmakers and their staff on the exchanges.