From this:

The federal government is not equipped to process the flood of applications from a proposed immigration legalization bill and the agency that would oversee that program won't be ready for "a few years," the office of the Homeland Security Department's inspector general told Congress on Tuesday.

The warning, from Assistant Inspector General Frank Deffer, could severely complicate President Obama's new push to pass an immigration bill this year.

Mr. Deffer said U.S. Citizenship and Immigration Services (USCIS), an agency of the Department of Homeland Security, is in the midst of trying to move from being a paper-based system to having electronic records. He warned that adding millions of new applications, as the bill would do, would be a bad idea.

"Adding 12 million more people to the system would be the mother of all backlogs. Clearly to us the systems could not handle it now," Mr. Deffer told the House Judiciary Committee's immigration subcommittee. "It's going to take a few years, so it's something for Congress to consider that, when they implement this, they don't have a date too soon."

On the other hand, Alejandro Mayorkas, director of the USCIS, said they were prepared: "We will be ready for comprehensive immigration reform when it is enacted." I lean towards Deffer being the more credible source.

Recall that back in 2006, a previous head of the USCIS said that the Senate's amnesty timeline wasn't practical. Around the same time, the GAO said the DHS wasn't prepared and didn't have a fraud management system in place.

And, from this:

A report released Dec. 20 [2006] by Homeland Security Inspector General Richard L. Skinner [note: he's still the IG] cited a long list of setbacks and concurred with internal USCIS reviews that the bureau "lacks the processing capacity, systems integration and project management resources needed to manage a potential increase in workloads."

Also see this from early 2008.