House conservatives will not support Senate Republican Leader Mitch McConnell's backup plan to raise the debt ceiling, a leading House conservative told "Fox News Sunday," calling it a "cop-out." 

Rep. Jim Jordan, R-Ohio, chairman of the Republican Study Committee, slammed a plan that is looking increasingly vital as deficit-reduction talks aimed at a "grand bargain" lose steam. With time running out to reach a deal and credit rating agencies warning the U.S. risks a credit downgrade, that backup plan would allow Congress to vote on incremental debt ceiling increases worth $2.5 trillion -- only in such a way that makes it easier for President Obama to win congressional permission. 

Jordan said he's not sure whether there's some combination of Republicans and Democrats that could get behind that plan and approve it. But he claimed his conservative House wing, as well as some Senate Republicans, will not be a part of any coalition. 

"They're not going to support the McConnell plan. I'm not going to support the McConnell plan," he said, pushing instead a House plan to cut and cap federal spending while requiring a balanced-budget amendment in exchange for a debt-ceiling increase. "This is just kicking the can down the road." 

Under the McConnell plan, instead of voting for the debt cap increase, Congress would vote on a "disapproval" resolution -- meaning that in order to block the president Congress would need to vote for the resolution, and then muster a two-thirds majority in both chambers to override a presidential veto. 

The proposal would presumably be tied to more than $1 trillion in spending cuts, and make way for a new budget-balancing commission. 

But some Republicans have doubts that the split approach could yield the kind of deficit reduction they're looking for. And while Democratic leaders say they're willing to work with McConnell on the concept as a last resort, they say they don't like the idea either. 

"I'm not a fan of the Mitch McConnell deal," Rep. Chris Van Hollen, D-Md., ranking Democrat on the House Budget Committee, told "Fox News Sunday." "It does punt it." 

Van Hollen called the plan a "political answer, not a real answer to the problem." 

Asked whether he would support the plan if it were the only way to raise the debt ceiling, he said: "I'm working very hard so that that's not our only choice."