Price said he believes the government could absorb $85 billion in cuts — a roughly 2.5 percent cut to the budget.
"We've got to move forward at that level because we've got to bring spending down," he said.
But he advocated for a Republican plan that would allow the Obama administration to "select to a greater degree where that $85 billion in reductions would occur."
"The administration, appropriately, needs some more flexibility," Price said.
Republicans say that legislative change would allow the administration to prioritize cuts and protect vital services. But Democrats have maintained that such legislation is intended only to push blame for the sequester onto the White House — and that it would be impossible to shield the American people from seeing the impact of the cuts.
"There's no way around it," White House press secretary Jay Carney said Monday. "It can't be written off, not with the size of these cuts, and the fact that they needed to be implemented in such a short period of time in this fiscal year."