TOLEDO, Ohio — Republican presidential nominee Donald Trump is surging in the polls here, delighting his supporters who say they are surprised only that the press is publishing the good news. They are convinced Mr. Trump is fighting a two-front war against Democratic nominee Hillary Clinton and her allies in the news business.

Connie King, 53, a home-schooling mom who joined about 2,500 fellow supporters at a Trump rally in a performing arts theater here, said the grass-roots movement behind Mr. Trump was too big for the news media to continue to cover up.

“They’re finally giving up because they can’t hide the truth anymore,” she said. “I knew this was going to happen before he was nominated. The support has always been there.”

Mr. Trump has garnered strong support in this economically struggling city on the banks of Lake Erie, winning over blue-collar workers and other Democrats who often feel left behind by the economy and overlooked by politicians in Washington.

The strength of support for Mr. Trump in this solidly Democratic region has given his campaign and his supporters confidence that he will capture Ohio, a state that is key to his electoral strategy, in November.

At the rally, Mr. Trump touted his climbing numbers in the polls and said his success was rattling the Washington establishment.

“The Washington insiders are panicking. They are very concerned. They are looking at the polls and they are saying, ‘What’s happening? This wasn’t supposed to happen,’” said Mr. Trump. “But it’s happening, and we are going to go all the way.”

The numbers are encouraging for Mr. Trump. However, unless he musters a landslide victory, Mr. Trump faces a narrow path to the 270 electoral votes needed to win the presidency. He trails Mrs. Clinton in most national polls and in some key states, such as Pennsylvania.

“I personally think he’s up higher than polls are indicating. He’s got more votes out there then they are counting,” said Dick Reilly, 68, a retired electric utility supervisor who was volunteering at the rally.

Stay-at-home mom Randi Scovell, 38, said she knew why the polls did not show Mr. Trump with a larger lead. “It’s the media,” she said. “They just trample over him every chance they can.”

Accusations that the mainstream media is working to undermine the Trump campaign are not new. Mr. Trump promoted the idea since the start of his run, frequently telling his supporters that news reporters are “the most dishonest people you will ever meet.”

He also calls the press “scum” and “sleazy,” all of which were reliable applause lines at his rallies.

Mr. Trump dropped that bit from his stump speech this month when he started using a teleprompter and sticking to a script.

Still, his surge in polls in the final stretch of the race gave Mr. Trump’s supporters fresh evidence that he is beating not only Mrs. Clinton but also her friends in the press corps.

A Bloomberg poll of likely Ohio voters last week and a Fox News poll released Wednesday evening gave the New York businessman a 5-point lead in the state.

The Fox News poll of 737 likely voters was taken Sunday through Tuesday and had a 3.5 percentage point error margin. It showed Mr. Trump ahead of Mrs. Clinton by 42 percent to 37 percent in a four-way race, in which Libertarian nominee Gary Johnson got 6 percent and Green Party nominee Jill Stein had 2 percent. Reducing the race to a two-way contest did not significantly affect the result — Mr. Trump led 45 percent to 40 percent.

According to Fox pollsters, Mr. Trump’s edge “comes mainly from independents (+20 points) and working-class whites (+26).”

“Clinton’s mistakes on the campaign trail have driven many disaffected Republicans into Trump’s camp,” Fox pollster Daron Shaw said. “Just as consequential is the fact Trump is ahead of Clinton among independents by 17-20 points in these states. If that holds, he might actually pull this off.”

The Bloomberg survey, which had him up by 44 percent to 39 percent measured a four-way race, in which Libertarian nominee Gary Johnson got 10 percent and Green Party nominee Jill Stein was at 3 percent.

The Real Clear Politics average of recent polls in Ohio put Mr. Trump ahead by 2 points.

“If this continues, he’ll take Ohio and Pennsylvania, too,” said Trump supporter Steve Haremza, 65, a financial adviser in Maumee, Ohio, a suburb about 10 miles south of Toledo on the Maumee River. “You’ll be surprised to see what happens.”

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