House Republicans are touting a new plan that calls for temporarily resolving the debt-ceiling standoff and passing a bona-fide budget for the first time in years.

But lawmakers on both sides of the aisle are claiming there’s a problem – they say it’s unconstitutional.

In an effort to break the partisan deadlock, GOP leaders on Friday pitched an ultimatum aimed at the Democrat-controlled Senate. The plan, dubbed “no budget, no pay,” allows the government to get three more months of borrowing authority, with no immediate spending cuts required, in exchange for having to pass a budget within that time. If senators fail to do so, they will be denied their federal paychecks.

“We will authorize a three-month temporary debt limit increase to give the Senate and House time to pass a budget,” House Majority Leader Eric Cantor, R-Va., said. “Furthermore, if the Senate or House fails to pass a budget in that time, members of Congress will not be paid by the American people for failing to do their job.”

In selling the idea, House Speaker John Boehner called the Senate’s failure to pass a budget over the last four years “shameful.”

But the idea – formally unveiled Monday, teeing up a vote on Wednesday – is already drawing criticism from some Democrats and Republicans, who claim the provision on pay violates the Constitution. The 27th Amendment states that: "No law, varying the compensation for the services of the Senators and Representatives, shall take effect, until an election of Representatives shall have intervened.”

“I understand the sentiment behind ‘no budget, no pay,’” Rep. Hakeem Jeffries, D-N.Y., said Monday, but “it appears that the 27th Amendment does not permit Congress to alter its pay in the midst of a current session.”

“We just started the 113th Congress, effectively meaning that we would not be able to alter our pay or wouldn’t be able to take effect until 2015,” Jeffries told Fox News. “Even if this was presented, it would render it meaningless in terms of the effect it’s intended to have.”

Rep. Darrell Issa, R-Calif., was quoted as saying the plan is “unconstitutional” in an article published Friday by Roll Call. But in a subsequent statement sent to Fox News, the Republican lawmaker clarified his position, saying, “I strongly support the House Republican leadership's proposal to link the debt ceiling increase to passage of a budget by the Senate, which has gone 1360 days without passing a blueprint for federal spending.

“While the 27th Amendment prohibits Congress from varying its own pay within a given Congress, as I noted in my interview it can certainly withhold pay,” said Issa, who presides as chairman of the House Oversight and Government Reform Committee. “I expect the final proposal brought before the House will have resolved any constitutional questions and that it will have my support."

House Republican leadership is defending the plan. A GOP leadership aide told Fox News that members would ultimately get paid, since "constitutionally we have to pay members." The suggestion is that the plan would not violate the 27th Amendment because it would temporarily withhold pay, as opposed to reducing pay. Under the plan, members' pay would be put in escrow starting on April 15 for any chamber that hasn't passed a budget resolution. Meanwhile, the debt ceiling would be suspended through May 18.

Votes from Democrats may be necessary to pass the plan, if Republican conservatives who oppose any increase in the debt limit withhold their support.

The White House said it's "encouraged" by the apparent willingness to extend the debt limit. And Senate Majority Leader Harry Reid also welcomed the development -- but his office is indicating that Senate Democrats won't accept it because of the measure on congressional pay.

The conservative group American Majority Action, which has been highly critical of Boehner, also came out against the "no budget, no pay" plan, claiming last week that while it's "clever" it violates the 27th Amendment.

The Associated Press contributed to this report.