The chairman of the House Oversight and Government Reform Committee said constitutional problems may doom a debt ceiling plan announced earlier Friday by House leaders, but the Republican lawmaker said he has a replacement in mind.

“That’s unconstitutional,” Rep. Darrell Issa said of the plan to withhold members’ pay if their chamber does not pass a budget resolution. House Republicans have dubbed the proposal “no budget, no pay.” The plan includes an offer by House leaders to pass a three-month increase in the debt ceiling on the condition that Senate Democrats pass a budget.

But legality of the “no pay” part of the deal could run afoul of the 27th Amendment, which says: “No law, varying the compensation for the services of the Senators and Representatives, shall take effect, until an election of Representatives shall have intervened.”

GOP leadership aides said Friday the plan would only withhold pay until a budget is passed, allowing the prospective law to pass muster under the amendment.

Issa said that while Congress could temporarily withhold pay, the threat would essentially be empty because eventually members would have to receive their withheld pay in order for their compensation to not have been varied.

The California Republican is urging Speaker John A. Boehner to take up legislation he introduced to tie the debt ceiling increase to passage of the budget.

Within minutes of this story’s publication, Issa’s office released a “clarifying statement” attributable to the California Republican. “I strongly support the House Republican leadership’s proposal to link the debt ceiling increase to passage of a budget by the Senate,” the statement began, ending with, “I expect the final proposal brought before the House will have resolved any constitutional questions and that it will have my support.”

Under Issa’s proposal, formulated in the 1980s by former Democratic Rep. Richard A. Gephardt of Missouri, the debt ceiling would be increased to the projected amount of government borrowing that would be needed based on the level of revenues and spending set by a final budget adopted by both chambers.

An earlier version of this article mischaracterized the Gephardt Rule.