Donald Trump takes the stage for a campaign rally in Clive, Iowa, U.S., September 13, 2016. REUTERS/Mike Segar Donald Trump is closing in on Hillary Clinton in key swing states and making gains nationally, according to polls released Wednesday.

A Bloomberg Politics poll showed the Republican presidential nominee with a 5-point lead over his Democratic challenger in Ohio, and a CNN poll released the same day showed Trump with a similar lead in Ohio in a four-way race including Libertarian candidate Gary Johnson and Green Party candidate Jill Stein.

The CNN poll also shows Trump leading Clinton in another important swing state, Florida, with 47% of the vote to Clinton's 44% in a four-way race.

Trump is also cutting into Clinton's lead nationally. A Quinnipiac University poll released Wednesday showed Trump with 43% of the vote and Clinton with 48% among likely voters in a head-to-head race. Just last month, Clinton had a 10-point lead over Trump in the same poll.

The numbers get even dicier for Clinton when you factor Johnson and Stein into the race, with the election appearing to be in a near deadlock — when the Quinnipiac poll expanded to a four-way race, Clinton took 41% of the vote, Trump took 39%, Johnson took 13%, and Stein took 4%.

The polls came after a rocky weekend for Clinton. She abruptly left a 9/11 memorial service on Sunday after overheating related to previously undisclosed pneumonia, and on Saturday was forced to address a statement saying half of Trump supporters fell into a "basket of deplorables."

"No doubt the pneumonia will pass, but like a nagging cough that just won't go away, Donald Trump defies every remedy Hillary Clinton throws at him," Tim Malloy, assistant director of the Quinnipiac poll, said in a press release.

He continued: "It's the definition of 'damned by faint praise,' a presidential contest where a vote for a candidate is less an endorsement of that candidate than a stinging rejection of his or her opponent. Priority one for Hillary Clinton and Donald Trump as the election looms: lure the cynical, disaffected, downright disgusted electorate into their camp. That's no mean feat as clouds of distrust loom over both campaigns."

Clinton and Trump are the most unpopular presidential candidates in modern history, with record-high negative ratings from voters.

Maxwell Tani contributed to this report.