WASHINGTON — President Trump’s erratic handling of the coronavirus outbreak, the worsening economy and a cascade of ominous public and private polling have Republicans increasingly nervous that they are at risk of losing the presidency and the Senate if Mr. Trump does not put the nation on a radically improved course.

The scale of the G.O.P.’s challenge has crystallized in the last week. With 26 million Americans now having filed for unemployment benefits, Mr. Trump’s standing in states that he carried in 2016 looks increasingly wobbly: New surveys show him trailing significantly in battleground states like Michigan and Pennsylvania, and he is even narrowly behind in must-win Florida.

Democrats raised substantially more money than Republicans did in the first quarter in the most pivotal congressional races, according to recent campaign finance reports. And while Mr. Trump is well ahead in money compared with the presumptive Democratic nominee, Joseph R. Biden Jr., Democratic donors are only beginning to focus on the general election, and several super PACs plan to spend heavily on behalf of him and the party.

Perhaps most significantly, Mr. Trump’s single best advantage as an incumbent — his access to the bully pulpit — has effectively become a platform for self-sabotage.