GALESBURG, Ill. — President Obama waved aside persistent Republican criticism of his signature health care law last week, saying in a New York Times interview that the overhaul would become vastly more popular once “all the nightmare scenarios” from his adversaries proved wrong.

The president accused Republicans of “all kinds of distortions” about the legislation. He said bluntly that his administration had a simple plan to build support for the law, which continues to be viewed with suspicion by large numbers of Americans. “We’re going to implement it,” he said.

Mr. Obama said he decided to delay a requirement that businesses provide insurance to their employees because of concerns expressed by executives about its administrative burdens. Some companies that already provide insurance had balked at provisions requiring them to show proof. The president said delaying that part of the law for a year would give the Treasury Department and other agencies a chance to make it “a little bit simpler” for companies to comply.

But he rejected criticism that by delaying the provision he had exceeded his constitutional authority.