The “Republican DREAM Act” proposed Sen. Marco Rubio (R-Fla.) is a challenge to President Obama on immigration policy, but also a challenge to his own party, which has shied away from immigration reform in favor of border security.

There’s good reason for that. Even as illegal immigration has declined, public concern about the issue and desire for increased border security has stayed high.

For the first time since the Depression, more Mexicans are leaving the United States than coming in, according to a Pew study out this week. The number of undocumented immigrants in the country dropped from 7 million in 2011 to 6.1 million in 2001.

The recession, combined with a declining birth rate in Mexico and increased deportations in the U.S., appears to have slowed illegal immigration down to a trickle. Border Patrol apprehensions — a common gauge of how many people are attempting to enter the country illegally — declined 61 percent from 2005 to 2010.

Yet during that same five years, at least three-quarters of Americans believed the government was not doing enough to stop illegal immigration, according to Washington Post surveys. Arizona’s controversial immigration policy continues to be popular. Even as the number of immigrants has declined, in CBS/NYT polling the number of people who considered immigration “a very serious problem” has increased.

Republicans in particular are inclined to favor border security alone. House Speaker John Boehner (R-Ohio) suggested today that it would be “difficult at best” for Rubio’s plan to pass the current Congress though he “found it of interest” — not exactly high praise.

“I’m not sure people have a sense that immigration is down,” said Joshua Uliberri of the Democratic polling firm Lake Research Partners. In states with large Hispanic populations, “it hasn’t penetrated their view of the issue.”

Whit Ayres, a Republican pollster at Resurgent Republic, agreed. “A change in the data is not likely to change opinions,” he said. People worried about illegal immigration “would be more likely to trust governors” in border states over polling or the administration.

Border-state Republican governors are not likely to spend much time defending the Obama administration. In the presidential primary, Obama was repeatedly attacked as insufficiently tough on border security. Texas Gov. Rick Perry repeatedly struggled to defend his support for in-state college tuition for undocumented immigrants.

But there are some signs of local shifts. In Arizona, the L.A. Times reported recently, the drop in illegal immigrants has cooled tempers. While 60 percent of Arizonans still support the state’s harsh policies, 65 percent also support the original DREAM Act, which would give undocumented immigrants in the military or college a path to citizenship.

Rubio’s plan offers non-immigrant visas with a chance at residency, not citizenship. Even that step is controversial among Republicans. If he can sell it to his own party, it would be a sign that public opinion is starting to catch up with facts on the ground.