A number of liberal Democrats are angry that Obama's budget includes chained CPI, a formula that would apply across the government and likely result in both entitlement cuts and tax increases.
Clyburn pointed out that he was on the bipartisan supercommittee that attempted to strike a deficit-reduction deal in 2011, and said his views are the same now as they were then: that changes in Medicare and Medicaid could be part of a grand bargain but that Social Security should be dealt with separately.
He demurred when asked whether he would vote against the president's budget if it were brought to a vote on the House floor.
"I don't think the president's budget is ever going to come to the floor of the House. If I did I'd be studying it right now. There's no need to clutter my mind with that. I need to focus on what [Chairman Paul] Ryan introduces in the Budget Committee so I can figure out how particularly I can vote no," he said.
"I'm not opposed to the [Obama] budget," Clyburn said. "I don't agree to the budget as it was proposed. And the president himself said this budget is not an ideal budget. He himself said what he's got there he's willing to consider as part of a big bargain."
House Minority Leader Nancy Pelosi (D-Calif.) also criticized chained CPI on Thursday, though she voiced support for the overall proposal.
"I myself believe that whatever we talk about in terms of prolonging [the] life of Social Security should be considered in its own place," Pelosi said during a Thursday press briefing at the Capitol.
"Whatever we're doing, it's about extending the life and the strength of Social Security. It's not about balancing the budget. That's some of the concern that some of our members have: Why is this in this bill?"