Sen. Jim DeMint (R-S.C.) on Wednesday rejected a fallback plan from Minority Leader Mitch McConnellAddison (Mitch) Mitchell McConnellGrassley, Wyden reach deal to lower drug prices The Hill's Morning Report — Trump applauds two-year budget deal with 0 billion spending hike Harris, Nadler introduce bill to decriminalize marijuana MORE (R-Ky.) that would give President Obama the power to raise the debt ceiling.

DeMint said Republicans will continue to push for a debt-ceiling package that cuts and caps federal spending, and he rejected accusations from Democrats that the GOP is standing in the way of a deal.

"This idea that Republicans will not vote to increase the debt limit is wrong," DeMint said.


Asked for his thoughts on McConnell's proposed fail-safe plan, DeMint said, "Republicans weren't elected last November to make it easier to spend and borrow and add to our debt."

McConnell's plan would authorize President Obama to raise the debt ceiling but would give Congress the power to block him with a resolution of disapproval. 

Lawmakers are struggling to strike a deal to raise the debt ceiling by the Aug. 2 deadline set by the Treasury Department. McConnell pitched his plan as a last resort if lawmakers cannot reach an agreement in time to avoid default. 

But DeMint said Republicans aren't giving up. He said he has been working House members and Senators on a new budget proposal that would be released in the next few days. 

"We're going to introduce a plan that would give the president an increase in the debt limit, but it's contingent on cutting spending and capping spending over several years, and giving the states the opportunity to decide if we're going to balance our budget in the next decade," DeMint said on CBS News.

"It doesn't make sense to continue putting just everything on the table that we want and then borrowing more money to do it."