A ne w survey of the country’s cultural and political landscape found that support for impeaching and removing President Trump from office is rising among most Americans, but that Republicans remain almost unanimously opposed, leaving Mr. Trump with a loyal but shrinking core of supporters.

The findings, released on Monday by the Public Religion Research Institute, a nonpartisan nonprofit based in Washington, also pointed to striking divisions among Republicans themselves, with white evangelical Christians and those who regularly get their information from Fox News forming a distinct and exceedingly devoted base of support for the president — many of whom say that there is virtually nothing he could do to make them lose faith in him.

Ninety-nine percent of white evangelicals and 98 percent of Republicans who rely on Fox News as their primary news source do not believe Mr. Trump should be impeached and removed, the survey found, compared with 94 percent of Republicans over all.

As committed as those Americans are to Mr. Trump, they alone are not enough for him to win re-election next year. And the survey revealed significant defections among some non-Republican constituencies that helped Mr. Trump win in 2016, namely the white working class. This trend is driven by white women without a college degree, 40 percent of whom now say they support impeaching and removing him, compared with 29 percent who said so in mid-September.