“We just spent the last three months talking about nothing else but ObamaCare. It has been on the front page of every newspaper. The polls show ObamaCare’s more unpopular than ever. People are starting to wake up that it isn’t going to work at all,” he says. “Even Jon Stewart of ‘The Daily Show’ is making fun of the law.” On Monday, Mr. Stewart had Health and Human Services Secretary Kathleen Sebelius as a guest, Mr. Needham notes, and the host “bet that he could download every movie ever made before she could log on to the ObamaCare website.”

Has the House GOP strategy gone at all awry? Mr. Needham says no. “If conservative groups like Heritage Action hadn’t raised the stakes on ObamaCare,” he says, “we’d be debating on their side of the football field talking about tax increases, gun control, more spending and amnesty for illegal immigrants.” He notes that in addition to remaining steadfast on defunding ObamaCare, he and his allies are also supporting conservative goals such as preserving the spending caps and budget sequester.

Mr. Needham is not apologetic at all for the shutdown that he sees as regrettable but necessary collateral damage if it focuses the public on the horrors of the health-care law. “I think people who don’t follow politics as closely as you and I do, which is most normal people, only pay attention when something major’s going on. Why is there a government shutdown going on? Because the Republican Party wants to get rid of ObamaCare,” says the highly disciplined Mr. Needham, who rarely strays from that message.