House Republicans said Friday that they will not agree to a long-term debt ceiling increase unless the Senate works with them to pass a budget deal. They will also withhold Congress’s paychecks if either chamber fails to adopt a budget by April 15.

“The principle is simple: No budget, no pay,” John A. Boehner (R-Ohio) said. The principle may be simple, but the legality of withholding lawmakers' checks is in doubt.

The 27th Amendment states, "No law, varying the compensation for the services of the Senators and Representatives, shall take effect, until an election of Representatives shall have intervened." Members can raise the salary of the next Congress, but they can't hike (or cut) their own pay.

A House Leadership aide said Republicans do not believe the provision would violate the Constitution because it would not reduce members' pay, but merely withhold it, pending passage of a budget. The liberal blog ThinkProgress argues that withholding pay amounts to varying it. No Labels, a non-partisan group that backs No Budget No Pay, argues that the pay withholding wouldn't take effect until the next Congress.

"I think that it's probably a cut and therefore it is a problem," said Michael Gerhardt, a constitutional law professor at the University of North Carolina. In a case involving federal judges, he noted, the U.S. Court of Appeals for the Federal Circuit declared that withholding a cost-of-living increase was cutting pay and therefore unconstitutional.

Both Democrats and Republicans have supported withholding pay in the past.

In 2011 the Senate passed by unanimous consent a bill, sponsored by Sen. Barbara Boxer (D-Calif.), that would stop congressional paychecks in the case of a government shutdown. The House attached the same language to a budget bill that could not pass the Senate, so the hold on pay never became law.

Rosalind S. Helderman contributed to this report.