In his weekly colloquy with Minority Whip Steny Hoyer (D-Md.), Cantor said Budget Committee Chairman Paul Ryan (R-Wis.) is still trying to work with Senate Budget Committee Chairwoman Patty Murray (D-Wash.) on the broad outlines of a deal. But he said those efforts are stymied because Democrats are looking to raise taxes.
Hoyer criticized the GOP position by saying Republicans are refusing to hold a conference "because there's disagreement on what the result of that conference will be."
Cantor said the GOP will hold to the position that the answer to reducing the budget deficit and the national debt cannot be tax increases.
"We would like to have agreement that we can begin discussions of a fiscally sane path to balancing our budget," Cantor said. "Our conference has made its stand, saying we want to balance the budget. We want to promote spending reductions and reforms that get us there in 10 years.
"And in that vein, we would like to see that it's not punishing the American taxpayer, the way that we get there … it's through growing our economy. It's reforming the kinds of things that are necessary to take care of those unfunded liabilities at the federal level."
The back-and-forth is the latest sign that the two sides are not close to an agreement to meet in conference, and that they would be unlikely to find a compromise budget plan even if they formed one.
Democrats are hoping a budget conference might find a way to repeal the sequester, which cut $80 billion from federal spending this year and requires another cut of about that size in 2014. Cantor said that Republicans also prefer to change the required cuts in the sequester, but said for now, it must be followed.
"Sequester is the law," he said. "That is our intention … to abide by the law with the sequester in place."
Cantor expressed only the general hope that the two parties can find a way forward on the budget, the sequester and the looming need to raise the debt ceiling.
"Hopefully we can all work together and come up with a way that we can adopt a plan that will manage down the debt and deficit and allow us to reach a balance in the federal level within 10 years," he said. But he added that Republicans are hoping to use these issues as a chance to reform programs that "we know are disproportionately causing the deficit."
That's a reference to entitlement reform, another issue that has led to wide disagreement between the two parties on how to reform programs like Medicare and Social Security.