One of these, the Department of Homeland Security Appropriations act, would spend $39.1 billion on the Department of Homeland Security, which represents a cut of $393.5 million, a 1 percent reduction from 2012 levels. More than half of that cut can be found in a $198 million reduction to TSA's passenger and screening operations program, which screens airline passengers around the country.

A report accompanying the legislation, H.R. 5855, says the bill does not take into account a pay raise for TSA workers, and would require 75 behavior detection officers to be let go.

Work on this bill comes just after a Senate committee approved its own Homeland Security bill that increases security fees for passengers from $2.50 to $5, which drew sharp opposition from airlines.

The Military Construction and Veterans Affairs and Related Agencies Appropriations act is by far the biggest bill, spending $146.4 billion in 2013. That's $10.8 billion more than current funding levels, and mostly reflects a 10 percent increase in funding for the Department of Veterans Affairs.

"The recommendation reflects the Committee's continued commitment to our servicemembers and veterans and to their families," House members said in their report for the bill, H.R. 5854.

The third bill is the Energy and Water Development and Related Agencies Appropriations act, H.R. 5325. That bill spends $32.1 billion, $87.5 million more than last year.

Within that bill, $26 billion is reserved for the Department of Energy, $345 million more than current year funding. But the bill cuts funding for the U.S. Army Corps of Engineers, the Department of the Interior, and an environmental cleanup fund.

The House Rules Committee is expected to approve one rule for all of these bills, plus H.R. 5743, the Intelligence Authorization act, although the rule will allow for separate consideration of each bill.