Although this trend of slippage is happening most among white evangelicals, closely followed by minority evangelicals, it's actually true of all Christian denominations. This table shows the drop-off in support for citizenship for illegal immigrants across denominations:

Support for a Path to Citizenship Among Religious Groups

This is all the more remarkable because these numbers came from a callback survey—meaning the very same people who gave their opinions in 2013 gave them again in 2014. In general, Americans feel pretty strongly about the issue: In both surveys, roughly a quarter of of respondents felt that immigration reform should be the country's top policy priority, and another 47 percent said it should be among the highest. In general, there have been few other shifts in attitudes toward immigration in the past year, which hints that this slight downward trend among evangelicals might be about more than frustration with Washington.

One possibility is that lay born-again Christians' opinions are shaped by factors other than faith. Across the survey, race seemed to influence views on immigration, and the same was true among evangelicals. Fifty-four percent of minorities supported paths to citizenship, compared to 48 percent of their white counterparts. Evangelicals are also more likely to have conservative, Republican-leaning views than any other religious group—so it may be that the party, not the pastor, is the main source of influence here.

The report's authors noted one other fascinating source of influence: Fox News. Evangelical Republicans and non-Republicans were equally likely to oppose a path to citizenship, but disciples of Hannity and other "fair and balanced" shows felt the most strongly:

Support for Immigration Reform Among Evangelicals Who Do and Don't Watch Fox News

The same doesn't seem to be true of evangelical leaders. Pastors at conservative Christian churches and the heads of evangelical organizations have been among the most vocal advocates for reform.

"I would not conclude that rank-and-file evangelicals are in a different place on immigration," Jones said. "But they may have less intense feelings about it than the leadership does. This issue is fairly low on the white evangelical priority list."

Salguero suggested it might be a question of education and communication. "If there’s any divergence, it’s in how much [congregants] know about this issue. As people get more acquainted with the issue, there has been a massive conversion among evangelicals in the pew."

Church involvement in immigration reform has been important in Washington, but increasingly, it's important for the congregations themselves: Among Hispanic Americans, evangelicals are the fastest growing religious group. In general, white evangelicals and minorities tend to have different political priorities—and as the demographics of the faith change, these differences will come into even greater relief.