"To have a 50 percent cut this year is going to put us at a severe disadvantage," King said. "And as we do approach the 10th anniversary of September 11, do we really want to cut our police departments, our counter-terrorism units, our intelligence units, our mass transit security, our port security by 50 percent? To me this is an invitation to an attack. We cannot put ourselves in that position."

King added that the terrorist threat level is as high now as it has been since the 9/11 attacks, and said the death of Osama bin Laden is likely to keep the threat level high.

Broadly, the bill cuts about $1 billion in DHS funding compared to FY 2011. About half of that cut comes from a $460 million cut to grants for firefighter assistance.

Members began debating amendments to the bill at about 4:20 p.m. -- an unlimited amendments are being permitted under the first open rule in nearly four years.

They started with an amendment from Reps. Steve LaTourette (R-Ohio) and Bill Pascrell (D-NJ) that would restore funding for grants by taking funds away from DHS management funding. Rep. Robet Aderholt (R-Ala.) said he has to "reluctantly" oppose the amendment because DHS management funds have already been cut.

Rep. David Price (D-NC) also has two amendments that seek to restore the firefighter assistance grants. The House is expected to work on the bill at least until Thursday.