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White House Press Secretary Sean Spicer holds the daily press briefing in the James Brady Press Briefing Room at the White House, January 23, 2017 in Washington, D.C. Getty Images

President Donald Trump has made a habit of criticizing the media, calling both stories and news outlets he doesn't like "fake news" and declaring the press the "enemy of the people." While some bristle at the idea of the president of the United States attacking the fourth estate, it would appear that Trump's base doesn't actually think a free press is all that necessary.

In a new poll, only 49 percent of Republicans and people who lean Republican said it was very important for American democracy that "news organizations are free to criticize political leaders." The poll, which was published Thursday by the Pew Research Center, found that 76 percent of Democrats and Democrat-leaning respondents said the free press was an important part of maintaining a strong democracy.

Pollsters also asked people if the right of the people to nonviolently protest was important, and 68 percent of Republicans and Republican leaners said it was, compared to 88 percent of Democrats and Democratic leaners. Pollsters also asked if it was important that "rights of people with unpopular views are protected." Eighty percent of Democrats and Democratic leaners agreed with that statement, while just 66 percent of Republicans and Republican leaners said unpopular views should be protected.

In two other questions about the components of a strong democracy, the partisan divide disappeared. Eighty-three percent of Republicans and 85 percent of Democrats said it was very important to have a "system of checks and balances dividing power between the president, Congress and the courts." Republicans valued "open and fair" national elections slightly more than Democrats, 92 to 90 percent, respectively.

The poll surveyed 1,503 people between Feb. 7 and 12.

While Trump continues to hammer the credibility of the media both on Twitter and during speeches, it does seem that Americans still trust the media more than the president. A Quinnipiac University poll released last week found that 52 percent of respondents trust the news media over Trump, while just 37 percent trust the president more.

But when it comes to Republicans, 78 percent trust the president more than the media, with just 13 percent of Republicans choosing to believe the media over the president. Only seven percent of Democrats trusted the president more than the media, the poll said.