By Amanda Becker

GREENSBORO, N.C. (Reuters) - Hillary Clinton got back on the campaign trail on Thursday after taking three days off for pneumonia, and the Democratic presidential candidate faced a more challenging political landscape, with Republican rival Donald Trump rising in opinion polls.

Senior Clinton aides said they always expected the race to the Nov. 8 election to be close. But it was clear from a raft of new polls that Trump had halted a summer swoon after taking steps to give a less freewheeling, more polished performance on the stump.

Clinton, 68, appeared in good health on a visit to her campaign plane's press cabin while flying to Greensboro, North Carolina, for a rally where she sought to refocus her campaign on the plight of the working class - which has turned out to be a potent theme for Trump.

Leaving the stage to the tune of James Brown's "I feel good," Clinton told reporters she kept her pneumonia diagnosis last Friday quiet, telling only senior staff, because she thought she would be able to "power through" the illness and keep campaigning.

"From my perspective, I thought I was going to be fine and I thought that there was no reason to make a big fuss about it," she said.

On Sunday, Clinton nearly collapsed while leaving a ceremony marking the Sept. 11, 2001, attacks in New York.

Her illness coincided with a mini-surge by Trump, who has drawn even or taken a slight lead in national polls. Polls in battleground states where the race is likely to be decided showed Trump now leading in Iowa, Ohio, Florida and Nevada, and tied in North Carolina.

Following her appearance in North Carolina, Clinton was scheduled to appear at a Washington dinner.

Clinton's campaign chairman, John Podesta, said the candidate and her aides expected the contest to be close.

"We always expected the race to tighten up, we still feel like we’re in a strong position with organizational advantage in Florida and Ohio," Podesta told reporters on Thursday. "They call these states battlegrounds for a reason."

In a speech at the New York Economic Club, Trump stuck to his script, avoiding the more improvisational style that has produced a cornucopia of controversies.

Trump pushed a package of tax cuts he said would help power the U.S. economy to an annual growth rate of 3.5 percent.

The New York businessman said his goal would be 4 percent growth, a target originally championed by Republican primary rival Jeb Bush. Trump said the growth would generate 25 million new jobs.

His economic package resurrected a decades-old debate on whether tax cuts can generate sustainable growth. But the overarching impression left by his speech was one of Trump talking about substantive issues and avoiding the frivolous.

Bob Shrum, a Democratic strategist who managed 2004 candidate John Kerry's unsuccessful campaign, said Clinton remained the favorite to win the White House, with demographic changes favoring her over Trump, who is heavily reliant on white voters.

What has hurt Clinton, Shrum said, is not the time taken off from the campaign trail but rather her decision to keep her diagnosis secret until forced to disclose it - which reinforced a perception among voters that she has a penchant for secrecy.

"Fairly or unfairly, what this was taken as was more evidence that she was not transparent and that’s what hurts her," Shrum said. "She been far more transparent than Trump but she hasn’t gotten any credit for it."

Democrats have sought to pressure Trump to release his tax returns, but the Republican has said he will not release them until a federal government audit has been completed. Clinton has released her tax records.

With the candidates' health in the spotlight, Trump, 70, on Thursday released details of a recent physical examination, a day after Clinton released specifics on her medical condition.

Trump's campaign said the results of his physical showed the fast-food fan has normal cholesterol with the help of a statin drug, weighs 236 pounds (107 kg) and has normal blood pressure.

In a not-so-subtle slap at Clinton, the Trump campaign said his medical report showed he "has the stamina to endure — uninterrupted — the rigors of a punishing and unprecedented presidential campaign and, more importantly, the singularly demanding job of president of the United States."

Trump also appeared on the "Dr. Oz Show" to discuss his health in an interview with host Mehmet Oz, a surgeon.

Top Clinton aide Jennifer Palmieri said "one upside" of Clinton's unplanned break was the chance to "sharpen the final argument Clinton will present to voters in these closing weeks."

"Our campaign readily admits that running against a candidate as controversial as Donald Trump means it is harder to be heard on what you aspire for the country's future, and it is incumbent on us to work harder," Palmieri said in a statement.

Trump backers on Capitol Hill said they were heartened by the tightening race after a call on Thursday morning with his campaign manager, Kellyanne Conway, who mapped out what the campaign was doing. She promised a more policy-driven approach from Trump in the race's final stretch.

"The poll numbers are just looking phenomenal as you move away from registered voters to likely voters," Republican U.S. Representative Blake Farenthold of Texas said.

(Additional reporting by Alana Wise and Ginger Gibson in Washington and Emily Stephenson in New York; writing by Steve Holland)