Biden Jr., his campaign is spending heavily in states, like Ohio, that it had hoped would not be competitive at all this year.

President Trump is facing the bleakest outlook for his re-election bid so far, with his polling numbers plunging in both public and private surveys and his campaign beginning to worry about his standing in states like Ohio and Iowa that he carried by wide margins four years ago.

The Trump campaign has recently undertaken a multimillion-dollar advertising effort in those two states as well as Arizona in hopes of improving his standing, while also shaking up his political operation and turning new attention to states like Georgia that were once considered reliably Republican.

Trump has expressed concern that his campaign is not battle-ready for the general election, while Republicans are concerned about whether the president can emerge in a strong position from the national crises battering the country.

Trump’s campaign, the president is now well behind Mr.

Biden, the former vice president, by double-digit margins, including a Monmouth University poll published on Wednesday that showed Mr.

Trump’s campaign, said in a statement that the race remained highly competitive.

“Our internal data consistently shows the president running strong against a defined Joe Biden in all of our key states,” Mr.

Trump’s belligerent response to protests after the killing of George Floyd, a black man, while in the custody of white police officers in Minneapolis, appears to have worsened his political position even further, officials in both parties said.

Over the past few weeks, the president’s operation has spent about $1.7 million on advertising in just three states he carried in 2016 — Ohio, Iowa and Arizona — that it had hoped would not be competitive at all this year.

Perhaps just as telling were two trips last month to Georgia by Vice President Mike Pence.

Trump’s map even if he were to hold other battleground states like Florida, North Carolina and Wisconsin.

The former vice president held a nine-point lead in Wisconsin, where Mr.

Aaron Pickrell, a Democratic strategist in Ohio who helped steer former President Barack Obama’s campaigns there, said Mr.

“I don’t think anybody will dispute the fact that if Trump loses Ohio, there’s no path at all,” Mr.

“We’re not going to be a tipping-point state this time, but I think Joe Biden can win here and I think the Trump campaign sees that.”.

Trump among a sliver of suburban Republican primary voters who could doom him altogether if they were to shift to Mr.

In a few states with primary elections this week, a smattering of suburban counties registered substantial, though far from strong, protest votes against the president from his fellow Republicans.

In Maryland, for instance, more than a tenth of Republican primary voters cast their ballots for Bill Weld, the former governor of Massachusetts who ended his quixotic campaign in March after registering in the low single digits in a string of primaries.

And his advisers point to the relatively high turnout on the Republican side in some states, like New Mexico, as a sign that Mr.

Biden, people familiar with the efforts said, even as other Republican and nonpartisan polling showed the president’s numbers stagnant.

Biden raised nearly as much money as the president in April.

Trump has said to allies, taking a decidedly different view of the Biden campaign than most Republicans as well as a good number of Democrats.