WASHINGTON — When Deborah Frank Feinen, the mayor of Champaign, Ill., drafted an emergency powers declaration last Thursday to confront the coronavirus pandemic, she was proud of her city’s early preparation. But by the time she got to work the next morning, the National Rifle Association had blared a “national alert” saying “anti-gun extremists” were moving “to undermine our firearms freedom.”

The city government was soon under siege.

“We were talking about how to get food to kids when schools were closed, and suddenly I’m getting Facebook messages about how I’m violating the Constitution and taking away people’s rights,” Ms. Feinen said in an interview. Now, in addition to working on plans for fire and police departments, emergency supplies, and helping small businesses weather state-mandated closures, “I’m obsessively looking at my email, checking for threats.”

Keen to defend President Trump from criticism and portray virus-related warnings as politically motivated fear-mongering, conservative organizations, media and Trump loyalists are undermining state and local government efforts to convey accurate information and protect their constituents.

An NBC News-Wall Street Journal poll conducted last week found that 81 percent of Republican voters said Mr. Trump has done well in handling the coronavirus crisis, and 84 percent of Democrats said the opposite. More than half of Republicans — 54 percent — worried that government will go too far in responding to the crisis, while just 31 percent of Democrats did, according to the poll.