House Republicans will not give up a plan to cut Medicare and eventually turn it over to the private market.

The Washington Post reported that House Majority Leader Eric Cantor (R-VA) suggested Wednesday that Republicans were open to budget talks with the White House, including taking Medicare cuts off the table.

But Cantor's chief spokesman, Brad Dayspring, disputed the report, saying that the congressman planned to stick to the budget introduced by Budget Committee Chairman Paul Ryan that would cut trillions in spending while lowering tax rates for corporations and high income earners.

"The Ryan budget which -- as you know -- assumes a debt limit increase and includes Medicare, Medicaid and $715 billion in mandatory savings," Dayspring told the Huffington Post. "Whether the Democrats will agree to the proposals we've outlined is yet to be seen, but that is our starting point so we don't continue to kick the can down the road and make real cuts and real reforms this year."

Sen. Kent Conrad (D-ND), who is retiring next year, announced Tuesday that he's preparing a budget plan that aims to cut $4 trillion from federal spending over ten years, in a way that mirrors the White House fiscal commission. Though short on specifics, it seeks to protect Medicare while achieving $1 trillion in savings through tax reforms, presumably by eliminating loopholes and deductions rather than raising rates.

The blueprint is notably more conservative than the plan President Barack Obama laid out in response to the House GOP proposal. Democrats privately fear that it could become the left foil to the Republican measure, establishing their flank much further to the right than they'd like it to be, and pave the way for a very conservative centrist compromise.

The budget battle comes as the United States fast-approaches its debt ceiling. Republicans have refused to raise the debt ceiling if Democrats don't agree to deep cuts to federal spending.

Economists have warned of a catastrophe if the United States fails to meets its obligations -- a collapse in the financial markets, massive layoffs due to a plunge in consumer demand and a possible depression.

Updated May 5th, 1:23am EST

With prior reporting by Sahil Kapur