Mr. Carlson, Ms. Ingraham and guests on their programs have said on the air that the vaccines could be dangerous; that people are justified in refusing them; and that public authorities have overstepped in their attempts to deliver them. Mr. Carlson and Ms. Ingraham last week criticized a plan by the Biden administration to increase vaccinations by having health care workers and volunteers go door to door to try to persuade the reluctant to get shots... Served up to an audience that is more likely than the general population to be wary of Covid vaccines, the remarks by Mr. Carlson and Ms. Ingraham echoed a now-common conservative talking point — that the government-led effort to raise vaccination rates amounted to a violation of civil liberties and a waste of taxpayer dollars. The comments by the Fox News hosts and their guests may have also helped cement vaccine skepticism in the conservative mainstream, even as the Biden administration’s campaign to inoculate the public is running into resistance in many parts of the country.