Throughout the week, the House has accepted something short of $600 billion in cuts, but has rejected $4.6 billion in proposed cuts. Jordan's bill would cut 5.5 percent from all agencies except the Department of Homeland Security, and would cut 11 percent from Congress's own appropriation.

Under the unanimous consent agreement, Jordan's amendment will get 30 minutes of debate. Another amendment from Rep. Steven LaTourette (R-Ohio) that would cut various agency budgets, some as much as 30 percent, will be considered for 30 minutes.

Four other amendments will be debated for 20 minutes: preventing the lease of Outer Continental Shelf areas for oil or gas production, blocking the transfer of prisoners at Guantanamo Bay, stopping the Environmental Protection Agency from enforcing regulations related to various pollutants and preventing enforcement of certain activities under the Consumer Product Safety Act.

One amendment from Rep. Steve King (R-Iowa), which would prevent enforcement of wage-rate requirements, will get 40 minutes of debate. And an amendment from Rep. Denny Rehberg (R-Mont.), which would prevent funds from being used to enforce last year's healthcare law, will get 60 minutes of debate.

About 120 other amendments can be debated for up to 10 minutes, but it was not clear that all of these amendments would be taken up.