Here's what Donald Trump supporters really believe

Donald Trump is still dominating his Republican rivals.

A new Public Policy Polling poll released on Tuesday shows Trump leading his GOP opponents by a familiar wide margin - 29% of likely GOP primary voters nationwide support the real-estate magnate.

Trailing him is the retired neurosurgeon Ben Carson, with 15% of the Republican vote. Former Gov. Jeb Bush of Florida comes in third with 9%.

But the new PPP poll also reveals some of the sentiments behind Trump supporters, including their desire to raise the minimum wage and skepticism of President Barack Obama's religion and birthplace.

Here are the main points from PPP:

• 66% of respondents who support Trump believe that Obama is Muslim, while only 12% believe that Obama is Christian. That's a higher number than the still stunning 54% of Republican respondents overall who believe that Obama is Muslim.
• Trump still enjoys support among "birthers" - 61% of supporters believe that Obama was not born in the United States. Just 21% of his supporters believe that Obama was born in the United States. Trump, once the most vocal advocate calling on Obama to release his birth certificate, has said he will no longer comment on the issue. But he has said he doesn't know whether Obama was born in the US.
• 63% of Trump voters would support changing the Constitution to eliminate birthright citizenship, the policy that automatically grants US citizenship to anyone born in the country. Twenty percent of Trump backers would not.
• Trump supporters really like Carson, former Hewlett Packard CEO Carly Fiorina, and Sen. Ted Cruz of Texas. Fifty-four percent said they held a favorable view of Carson, and 49% said they had a favorable opinion of both Cruz and Fiorina. Only 22% of Trump supporters held a favorable opinion of Bush.
• Most Trump backers support raising the minimum wage. Fifty-four percent responded that they favored raising the minimum wage, though the vast majority only supported an increase to $10 an hour.
• Trump supporters don't like Fox News host Megyn Kelly. Only 20% hold a favorable view of Kelly, though that is somewhat unsurprising considering Trump's ongoing beef with Kelly and her network. Trump supporters also overwhelmingly trust Trump over Fox News in general, while supporters of virtually every other candidate trust the network far more.
• Supporters are split over whether they value a conservative candidate or an electable candidate more. Trump backers were split almost straight down the middle on the question of whether it was more important to have a conservative nominee or a nominee who had a shot of winning in the general election.

The polling data backs up what some have observed anecdotally about Trump supporters over the past few months.

Business Insider attended a focus group of Trump supporters conducted by pollster Frank Luntz last week, and respondents overwhelmingly accused Republican leadership in Congress of acting like Democrats. The panel also fixated on media bias.

"The media and the establishment are deathly afraid of Trump," a member of the focus group said. "That's why I particularly love him. Because the media has become de facto the power behind the throne in this country."

Another panelist said: "Every time the media thinks it's got a 'gotcha,' he turns it around on them."