"I thought that was the height, height of stupidity, and I believe myself that he should go," Shelby told Bob Schieffer Sunday on CBS' "Face the Nation." "I don't know how he can represent a company in crisis like BP and ignore what's going on in the Gulf of Mexico."
Shelby also discussed his belief that President Obama should lift the moratorium on oil drilling in the Gulf. He said he understands both sides of the argument.
"We get about 30 percent of our oil from the Gulf now - that is the United States - we get a great percentage of that from the deep wells," he said.
"I believe that BP made some horrible mistakes, they probably tried to do it on the cheap," continued Shelby. "We have hundreds if not thousands of wells in the Gulf of Mexico. And we're probably going to need more and more. If we don't [lift the moratorium], the oil drilling will go [overseas] and maybe not come back for a long time.
"But we need hands-on regulation in this area," said Shelby. "The regulators have got to be on top of the industry, not the industry on top of the regulators," he added.
Republican Rep. Joseph Cao of Louisiana called for partial drilling instead of a total moratorium, something he cast as a compromise that would help ease the economic struggles the moratorium is causing for Gulf residents employed by the oil industry.
Partial drilling would "achieve both goals of allowing the administration the time to implement reviews, to implement new procedures and protocol, but at the same time to allow Louisiana to keep the jobs here," he said.
The way partial drilling works would be to allow people to keep building and digging wells, but have them stop just short of reaching oil. Cao noted that it takes three to four months to build a well.
"We can allow them to dig up to the first 12, 13-thousand feet and then ask them to stop, and they have the technology to do that," he said, arguing that the "moratorium is really making matters worse, and we have to find a common sense solution to this problem."
California Democratic Sen. Barbara Boxer said she is "open" to that idea but argued that drilling permit applications must be reassessed.
"I do believe that each permit must be looked at or we're going to be back to square one again," she said.
Along with Florida Democratic Sen. Bill Nelson, who also appeared on the program, Boxer called for the Navy to take over coordination of the beach and near-shore cleanup efforts.
Nelson said installing a "military command and control structure" would improve cleanup efforts that Gulf officials have deemed chaotic.