Earlier on Tuesday Paul proposed an amendment that would cut about five percent from government operations, which is the equivalent of $200 billion. The amendment has virtually no chance of meeting the 60-vote threshold required by Senate rules.
Inouye said those cuts would defund organizations like the Corporation for Public Broadcasting, National Public Radio and the National Endowment for the Arts.
Republicans in the House have already targeted each of these government expenditures for cuts. The House is scheduled to vote on defunding NPR on Thursday.
"Some agencies would not have sufficient resources to survive this cut," Inouye said.
The senior senator from Hawaii said the Department of Housing and Urban Development and the Office of Personal Management would also be forced to seriously curtail their operations under such a plan.