But Forbes opinion editor Avik Roy doesn't agree. "He [Donohue] didn't say that he opposes repeal," Roy says about Donohue's recent statement. "He just didn't think repeal was realistic in the next several years."
Business groups, such as the chamber, have to be pragmatic and deal with the world as it is, not as they'd like it to be, Roy says. That's why the chamber is now focusing on changing specific parts of the health care law that its members don't like, rather than repealing it.
Roy advised Mitt Romney on health policy in 2012. He thinks Republicans missed their chance to repeal the law in the 2012 elections. And they won't get another chance, he says, until after the 2016 elections. By then, the chance will be only small.
"It's very difficult, once a law that transformative has been in effect for seven years, to repeal it," Roy says. "I think there are more attractive ways to achieve the goals of conservatives than repeal and replace."
That strategy doesn't sound attractive or pragmatic to conservative talk show host Erick Erickson, who runs the Red State blog. Rather it sounds more like capitulation.
"The lobbying groups that have open access to Republican leaders are abandoning repeal," Erickson said in a recent podcast. "The wonks the GOP leaders listen to are abandoning repeal. They're laying the groundwork to bail on fighting Obamacare."
But both Roy and the chamber say they remain committed to fighting the health law. The chamber wants specific items thrown out, such as the requirement, beginning in 2015, that employers with more than 50 workers provide health insurance or pay a fine.
And Roy says conservatives could accomplish more by using Obamacare to push for transformation of all government-funded health care.
"The ACA is really an important, but smaller, portion of the overall reform picture," he says. "And I think what's happened with a lot of the more populist conservatives is that there's not necessarily that appreciation for how much the government is already involved in the health care system through programs like Medicare and Medicaid."
Conservative activist Erickson says the traditional Republican Party doesn't like its populist wing, and that it needs to be taught a lesson in the 2014 primary elections.
"The single biggest thing you can do to get the Republicans back on the right and straight path is to support Matt Bevin against Mitch McConnell in Kentucky," he said.
Erickson also urges financial contributions to conservative primary challengers in Georgia, Mississippi, Nebraska and other states. That means some Republican candidates will face heat from the right for not doing more to repeal Obamacare, while they're fighting Democrats who say they aren't doing enough to make the law work better.