"I think that's the real question, is whether that larger bill, which is sort of the Senate bill unaltered, will pass with a majority of Republicans," said Mulvaney on CNN's "Starting Point."
The House is expected to debate Hurricane Sandy relief package today, totaling $50.7 billion in recovery funding. On Monday the House Rules Committee approved a rule that blocked most of the GOP proposals to reduce the size of the bill.
Mulvaney introduced an amendment that would require a 1.63 percent cut to discretionary programs to make up for the $17 billion in spending in the main bill. The South Carolina lawmaker said separately Tuesday he doubts his amendment to offset the aid would be approved.
"I do think this a proper and appropriate function of the government. My difficulty with it is that it is simply not paid for. We're borrowing this additional money to do this and I just think that that's wrong," he said.
Mulvaney said he is hopefully that Congress will find savings in other areas in order to pay for Sandy relief without adding to the debt.
New Jersey Gov. Chris Christie (R) slammed Congress on Monday, saying that New Jersey was receiving different treatment than other states that have suffered natural disasters.
"New Jersey does not expect anything more than was done for Louisiana, and Alabama and Mississippi in Katrina, what was done in Joplin, Missouri, what was done in the floods in Iowa. We don't expect anything more than that, but we will not accept anything less and if they want to make new rules about disasters, well, they picked the wrong state to make the new rules with," said Christie.
Mulvaney said he understood Christie's concern, but argued that offsets are now needed to pay for natural disasters because the U.S. debt has ballooned in the years since Hurricane Katrina and other major disasters.
"We simply cannot continue to do what we've done in the past. That's how we arrived where we are. We have disasters every single year. We don't know where they are going to be, but we spend disaster money every single year. It's something for which we could budget," he said.
The South Carolina lawmaker emphasized that he is "not against" providing funding for Sandy recovery in New York and New Jersey, but said he wants Congress to take responsibility for paying for the funds.
"The question is not whether or not we're going to do this. We're obviously going to do this today. The question is whether or not it means enough to us to lawmakers to say that we're going to pay for it, because if we don't what we're essentially saying is our children are going to pay for it, and I think that's a debate we need to have," Mulvaney said.