Hours after he formally kicked off his 2020 re-election campaign, a new national poll offers some encouraging numbers for President Trump.

The release Wednesday of a Suffolk University survey for USA Today comes a day after another poll in the crucial presidential battleground state of Florida showed the president trailing -- and as several other polls have similarly shown high-profile Democratic candidates ahead.

THE LATEST POLLS FROM FOX NEWS

But the USA Today/Suffolk University survey showed 49 percent of Americans approving of the job Trump’s doing as president, with 48 percent giving him a thumbs down.

That’s a more positive showing for Trump compared with other recent polling of his presidential approval rating.

And in the new survey, 49 percent of voters predicted Trump would win re-election, with 38 percent pointing to a victory by the eventual Democratic presidential nominee. Further, the poll indicated that if the November 2020 general election were held today, the president would narrowly edge an unnamed Democratic nominee -- 40-37 percent, with 9 percent supporting an unnamed third-party candidate and 14 percent undecided.

That result differs from other recent national and early primary and caucus voting state polls, which indicate Trump trailing some of the leading Democratic White House hopefuls in hypothetical general election matchups. Trump's 2020 re-election campaign manager has slammed such non-partisan surveys as "the biggest joke in politics," and the president frequently rails against them.

Trump trailed former Vice President Joe Biden – the clear front-runner right now in the race for the Democratic nomination – 50-41 percent in a Quinnipiac University poll in Florida that was released on Tuesday. The survey also suggested Sen. Bernie Sanders of Vermont topping Trump 48-42 percent and Sen. Elizabeth Warren of Massachusetts ahead of the president 47-43 percent in hypothetical November 2020 showdowns.

"President Donald Trump trails both former Vice President Joseph Biden and Sen. Bernie Sanders in general election matchups and basically ties other leading Democratic challengers," Quinnipiac University poll assistant director Peter Brown said. "While most Florida voters are feeling better financially, President Trump remains underwater with a 44 percent job approval rating and a 51 percent disapproval rating."

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The Quinnipiac University poll was released a few hours before Trump kicked off his 2020 re-election bid in a jam-packed arena in Orlando. Trump edged Democratic presidential nominee Hillary Clinton in the 2016 election to capture Florida’s 29 electoral votes. Democratic President Barack Obama narrowly won the state in the 2008 and 2012 elections.

Trump's re-election campaign manager, Brad Parscale, is taking aim at such polls.

"The country is too complex now just to call a couple hundred people and ask them what they think. There are so many ways, and different people that are gonna show up to vote now," Parscale told CBS News. "The way turnout now works, the abilities that we have to turn out voters – the polling can't understand that. And that's why it was so wrong in 2016. It was 100 percent wrong. Nobody got it right. Not one public poll.”

TRUMP'S EYE POPPING SINGLE DAY FUNDRAISING HAUL

While Trump’s facing early warning signs in many national and early voting state polls, raising campaign cash has not been an issue. Trump’s re-election campaign and related committees raised an eye-popping $24.8 million in the 24 hours surrounding the president’s campaign kick-off, according to Republican National Committee chair Ronna McDaniel.

“@realDonaldTrump has raised a record breaking $24.8M in less than 24 hours for his re-election. The enthusiasm across the country for this President is unmatched and unlike anything we’ve ever seen! #trump2020 #KeepAmericaGreat,” McDaniel tweeted early Wednesday morning.

The USA Today/Suffolk University poll was conducted June 11-15, with 1,000 registered voters nationwide questioned by live telephone operators. The overall sampling error was plus or minus 3 percentage points.

The Quinnipiac University poll was conducted June 12-17, with 1,279 Florida voters questioned by live telephone operators. The overall sampling error is plus or minus 3.3 percentage points.