Obamacare had been deeply unpopular for its entire history, with more voters consistently telling pollsters they opposed the massive health care overhaul that Democrats pushed through Congress in 2010.

That is, until President Trump took office.

On Inauguration Day this year, Obamacare’s approval flipped from negative to positive in the Real Clear Politics average of polling, and it has never looked back. Despite Mr. Trump’s constant gibes, a stunning 51 percent of Americans now back the troubled health care law, according to Real Clear Politics, compared with 39 percent who oppose it.

Obamacare is just one of a number of issues where the public has flipped, and pollsters say Mr. Trump has a lot to do with it. He is chasing people away from issues, in part, just by supporting them.

“The psychology is easy. ‘I don’t like the guy. If he says two plus two is four, I’m going to make it five.’ That’s human nature,” said Michael McKenna, a Republican Party strategist and pollster. “The message and the messenger are inextricably linked.”

Perhaps most striking is how Mr. Trump has infected so many issues.

The Iran nuclear deal, which Mr. Trump mocks, is more popular than ever. The North American Free Trade Agreement, whose approval crumbled during the presidential campaign, is now firmly back in positive approval territory with Mr. Trump vowing to renegotiate it. The number of people who say they worry about global warming “a great deal” has soared this year.

Support for legalizing people in the country without authorization, which for most of this decade has hovered between 50 percent and 59 percent in Quinnipiac University polling, crossed the 60 percent support line this year and stood at 68 percent as of September. CNN’s polling shows similar trends, with support for legalization rising 9 percentage points after Mr. Trump took office.

Some of the issues have been trending in those directions for years, but the Trump bumps are all striking.

Analysts said some, such as Obamacare, could be explained by other factors such as the debate in Congress, but the broad range of issues suggests Mr. Trump is a major factor.

Mr. McKenna said tax reform is one example. The Republican legislation has many of the elements Democrats have talked about for years but is gaining no support from Democrats in Congress, nor in the public at large.

“If [President Obama] were coughing up this particular version of tax reform, 60 percent of people would love it,” Mr. McKenna said.

Longtime pollster John Zogby said all presidents have some effect on issues. When pollsters survey an issue and then ask the same question with the president’s name attached, the support for the president’s position usually drops.

During the tenure of President George W. Bush, asking about warrantless searches after pointing out that Mr. Bush backed it hurt support.

“Presidents, especially presidents that are controversial, just added an additional variable to the issue,” Mr. Zogby said. “When the issue is so closely associated with a president, then of course it has an impact.”

He said Mr. Trump is a particularly pointed case: With a majority of voters giving him low marks so early in his term, it’s spilling over into issues.

Mr. Zogby said there are hard-core Trump partisans and hard-core Trump resisters, but the real change has been among independent and moderate voters who have fled the president.

“He is a president who really has never sought the middle, and that’s important because that’s how you at least get to a majority by seeking the middle, or the leaners, or the undecideds,” the pollster said.

It’s impossible to know how much of the tilt in the numbers is because of Mr. Trump and how much is because of a changing public.

Gun control, which Mr. Trump has generally opposed as a candidate and while in office, is getting more popular — though a series of high-profile mass shootings is likely more of a factor than the president’s stance.

Still, on issues closely identified with Mr. Trump, such as immigration, polling had been fairly static until his emergence.

Polling has always been a touchy subject where Mr. Trump is concerned.

Indeed his very election, with victories in Pennsylvania, Michigan and Wisconsin, seemed to catch many pollsters off guard.

His job approval ratings lagged from the start of his term and have only become worse over time. The Real Clear Politics average found him with a 3 percent disapproval gap in early February, a 10-point gap in early May and a 21-point gap in the middle of this month, ahead of the tax cut bill’s approval.

His numbers showed a slight tick back upward as Republicans reached agreement on a final bill.

Mr. Trump was obsessed with his polling during the presidential campaign, regularly citing his numbers compared with other Republican candidates as signs of voter approval during the primary race.

He has quoted polls less frequently since taking office.

On Twitter, he did cite the occasional poll that showed his approval rising but dismissed others showing poor performance as “fake.”

“The Fake News refuses to talk about how Big and how Strong our BASE is,” the president said in a flurry of Christmas Eve tweets that blamed the press for giving Americans a distorted view of themselves, as well as his presidency.

“They show Fake Polls just like they report Fake News. Despite only negative reporting, we are doing well - nobody is going to beat us,” Mr. Trump tweeted.