Supporters of the healthcare law reject these concerns and say Republicans are using scare tactics for political gain.
The GOP lawmakers spoke on a call with reporters Tuesday. Several expressed disappointment that the latest House-passed bill to fund the government did not repeal healthcare reform.
Gingrey described how some Republican lawmakers are hesitant to back a partial repeal bill, worrying that it would make the rest of the law "palatable."
"But I think we should go full monty at chipping away at it … and weaken it, and weaken it, and weaken it," he said.
Lawmakers are working on a continuing resolution deal that would last through September, and the debt ceiling has to be raised this summer.
Tuesday's call was organized by FreedomWorks, a prominent Tea Party group.