Despite a growing sense that Republicans will bear most of public fallout from the government shutdown, some House conservatives still believe they will be vindicated in the end.

A story published Wednesday in The New York Times quoted a group of the hardline House Republicans leading the charge to halt the Affordable Care Act, an effort that helped trigger the first government shutdown since 1996.

Rep. Steve King (R-IA), in fact, still believes that the fight can lead to the “end of Obamacare.”

“We’ve passed the witching hour of midnight, and the sky didn’t fall, nothing caved in,” King told the Times. “Now the pressure will build on both sides, and the American people will weigh in.”

If recent polling is any indication, King may not want input from the public. According to findings released Tuesday from Quinnipiac University, 72 percent of Americans are opposed to shutting down the government to block implementation of the Affordable Care Act and 58 percent are opposed to Congress cutting off funding for the law. A CNN/ORC International poll released Monday showed that more Americans will blame Republicans than President Barack Obama for a shutdown.

But according to Rep. Raul Labrador (R-ID), Republicans won’t be in the doghouse for long.

“It’s getting better for us,” Labrador told the Times. “The moment where Republicans are least popular is right when the government shuts down. But when the president continues to say he’s unwilling to negotiate with the American people, when Harry Reid says he won’t even take things to conference, I don’t think the American people are going to take that too kindly.”