As a candidate, Donald Trump once joked, “I could stand in the middle of Fifth Avenue and shoot somebody and I wouldn’t lose any voters.”

A new poll tests how true that idea is. A sizable chunk of President Trump’s voters are nearly immovable: Around 15 percent of Americans say that they approve of Trump and that “there is almost nothing he could do to lose their support,” according to a new poll from the Public Religion Research Institute. A slightly larger share, 26 percent, approve of him but say they could change their minds.

Meanwhile, his opposition stands firmer: Thirty-three percent say that they disapprove of Trump and that “there is almost nothing he could do to win their support.”

PRRI conducted the survey from Oct. 18-30, and the margin of error for the full sample is 2.6 percentage points.

While Trump’s approval rating has held relatively steady recently, it has slid somewhat since he took office. At that time, his rating was just over 44 percent, according to the RealClearPolitics average. It hit bottom in August, at around 37 percent, but has flattened out since then. RealClearPolitics currently has the Trump approval rating at around 40 percent. This poll found an approval rating of 41 percent.

Trump’s low approvals have sparked questions about where his “floor” is — how low could his approval ratings go? PRRI’s 15 percent figure mirrors the 14 percent that YouGov and Huffington Post found in August when they asked a similar question.

The level of that support varies heavily by demographic group. Black Americans are some of Trump’s most fervent opponents, with 60 percent saying that they disapprove of the president and that almost nothing could persuade them to do otherwise — what PRRI calls “strong Trump opponents.” An additional 26 percent are “weak Trump opponents,” meaning they disapprove of the president but say he could win their support.

Women are another group bolstering the numbers of “strong Trump opponents.” Forty-one percent of women are strong Trump opponents, compared with just 24 percent of men.

Meanwhile, Trump has some of his strongest support among white evangelical Protestants, 30 percent of whom say they support him and probably won’t change their minds. Twenty-four percent of whites without college degrees are likewise “strong Trump supporters.”

While Republicans are among Trump’s staunchest supporters — with 84 percent saying they approve of his job performance — their support isn’t unbreakable. Thirty-four percent say there is little the president could do to lose their support, but a plurality — 50 percent — say that he could do something to shake their support.

The poll finds that a majority of Americans — 56 percent — do not support impeachment of the president. Forty percent do. These numbers are little changed from when PRRI last asked the question in August.