But all the law guarantees is a hearing, not amnesty. And the passage of a law promising a hearing to a large segment of illegal immigrants who would not otherwise be entitled to one ensured an increased workload for the immigration court system–a promise the U.S. government largely ignored.

“It’s sort of ironic the one part of the immigration system that is underfunded is the one that provides due process to immigrants,” said Daniel Costa, Director of Immigration Law and Policy Research for the Economic Policy Institute in Washington. In recent years, he said, funding for immigration enforcement operations increased 300 percent—that’s the part of the system charged with apprehending illegal immigrants and bringing them before a judge. Over the same time frame, Costa said, the funding for the courts rose only 70 percent.

Read More Obama on immigration: I’m going to fix as much as I can, on my own

“If there wasn’t an immigration court crisis, there wouldn’t really be a border crisis,” Costa said. “The crisis is that we can’t provide everybody with a hearing. If they were being processed in an orderly fashion–if their cases were being processed in 60, 90, or 100 days—I don’t know if people would be making so much noise about it.”

President Barack Obama’s $4 billion proposal to address the crisis on the border would allow for the hiring of a few dozen judges. A more expansive proposal being pushed by Sen. Barbara Mikulski would provide for substantially more. Given the backlog, though, there’s no likelihood, in the near term, of changing the impression many potential illegal immigrants have that, simply by crossing the border, they will get to stay in the U.S. indefinitely.

Reducing the backlog is going to take years, even with additional funding, Costa said. “Even if you to double or triple the immigration judges you aren’t going to do it overnight.”

Read MoreA year later, bright hopes quashed on immigration

—By Rob Garver, The Fiscal Times