The House of Representatives and Senate on Wednesday passed a last-minute stopgap spending bill that will keep the federal government open through Dec. 11 pending President Barack Obama's signature. But another budget battle will likely ensue then, as Congress remains divided over federal funding for women's health organization Planned Parenthood.
Read MoreHouse passes legislation to avoid shutdown
Many in Congress have opposed a shutdown, as a government closure can put some federal employees temporarily out of work or delay their pay. Stockman contends it could have a positive effect by making lawmakers address spending and debt issues.
He called for entitlement and defense spending reform. He also argued that easy monetary policy from central banks has made lawmakers less likely to address the deficit.
Still, Stockman did not clearly outline why a shutdown would force lawmakers to make significant budget changes.