As the White House-led debt-ceiling negotiations enter their final, contentious stretch, House Republicans on Friday introduced a new factor in the calculus by announcing that they will vote next week on a plan to “cut, cap and balance” the budget.

“The ‘cut, cap and balance plan’ that the House will vote on next week is a solid plan for moving forward,” House Speaker John Boehner (R-Ohio) said at a news conference Friday morning. “Let’s get through that vote and then we’ll make decisions about what will come after it.”

Speaking an hour before President Obama was to address reporters at a news conference, House Republican leaders took aim at the White House’s position in the ongoing debt-limit talks. House Majority Leader Eric Cantor (R-Va.) said that House Republicans have identified $6.2 trillion in deficit savings over the next 10 years while Democrats are at $1.5 trillion, “at best.”

“We’re in the fourth quarter here,” Boehner said. “Time and again, Republicans have offered serious proposals to cut spending and address these issues, and I think it’s time for the Democrats to get serious as well. We’ve asked the president to lead. We’ve asked him to put forward a plan – not a speech, a real plan – and he hasn’t. But we will.”

House Republican leaders announced the plan at an early-morning members-only conference meeting in a Capitol meeting room. Leaders in both chambers had already planned on holding votes on a balanced budget amendment to the Constitution next week; the “Cut, Cap and Balance Act” is a measure that would immediately cut spending, enact statutory spending caps and mandate that Congress pass a balanced budget amendment before it can vote to raise the country’s $14.3 trillion debt ceiling.

The move is likely to be a symbolic one, as Democrats in both chambers have expressed their opposition to a balanced budget amendment as currently drafted by House Republicans, arguing that its provision calling for a supermajority in both chambers to raise taxes is too stringent.

House Republicans’ announcement also throws further uncertainty in the road ahead on raising the debt limit, as many members of the House Republican rank-and-file after Friday morning’s conference meeting said they were opposed to a “back-up plan” proposed by Senate Minority Leader Mitch McConnell (R-Ky.) that would allow the debt ceiling to be raised.

“That’s [a plan] that maybe makes sense politically; I don’t think it makes sense to America,” said freshman Rep. Mike Kelly (R-Pa.), adding that some members at Friday’s meeting criticized the proposal as “the Pontius Pilate plan.”

“I’ve never been open to the plan. ... I’ve said a long time ago that ultimately, Article I, Section 8 of the Constitution says that only Congress has the power to borrow; I think we should stick with the Constitution,” said Rep. Tim Scott (R-S.C.), a freshman who is a member of leadership.

Even so, the leadership was not yet taking the option off the table.

“Senator McConnell pointed out that his plan was being put on the table as a last-ditch effort,” Boehner said. “We’re far from the time for a last-ditch effort.”

It’s possible that next week’s vote on the “cut, cap and balance” plan could pave the way for a future vote on a balanced budget amendment that would be more palatable to Democrats, such as one that would lower the threshold for tax increases.