Gohmert made the accusation during a speech at the annual Values Voters Summit in Washington, while criticizing McCain for having said earlier in the day Republicans shut down the federal government "on a fool's errand that we were not going to accomplish," to defund the Affordable Care Act.
"When it comes to the shutdown that's going on, I heard just before I came some senator from Arizona, uh, a guy that liked [former Libyan dictator Moammar] Gadhafi before he wanted to bomb him, a guy that liked [former Egyptian President Hosni] Mubarak before he wanted him out, a guy that's been to Syria and supported al-Qaida and rebels, but he was saying today the shutdown has been a fool's errand," Gohmert said, eliciting boos at the reference to McCain. "And I agree with him. The president and [Senate Majority Leader] Harry Reid should not have shut this government down!"
McCain made his remarks about the shutdown during an interview with Fox News, in which he criticized the White House for its handling of the budget and shutdown, but told Fox "a little straight talk" was needed.
"They wouldn't have had the opportunity to handle it that way if we had not shut down the government on a fool's errand that we were not going to accomplish," McCain said. "The whole premise of shutting down the government was the repeal of Obamacare."
An aide told The Hill McCain would not dignify Gohmert's remark about al-Qaida with a response.
During the Fox interview, McCain said Republicans "better wake up," in response to the latest NBC News/Wall Street Journal poll, showing 24 percent of Americans support Republicans, an all-time low.
"Defunding Obamacare is not achievable so let's not delude our supporters by telling them that it is under the present circumstance, because elections have consequences," he said.
McCain did, however, say entitlement and tax reform will be achieved during negotiations on extending the federal borrowing limit, set to expire next week.
"I guarantee it," he said.