In contrast, he said, the Jordan bill cuts "everything, indiscriminately, in a heavy-handed way."

Another Republican, Rep. Jo Bonner (R-Ala.), called the amendment is "misguided," and said cuts in the committee were done "surgically" with "deliberate intent."

"Across-the-board cuts are a lazy way to achieve something," added Rep. Dan Lungren (R-Calif.), and Rep. Bill Posey (R-Fla.) also spoke in opposition, saying the proposal would cut some national-security items. Reps. Rodney FrelinghuysenRodney Procter FrelinghuysenThe 31 Trump districts that will determine the next House majority Top House GOP appropriations staffer moves to lobbying shop Individuals with significant disabilities need hope and action MORE (R-N.J.), Frank WolfFrank Rudolph WolfDOJ opinion will help protect kids from dangers of online gambling Vulnerable Republican keeps focus as Democrats highlight Trump Bolton could be the first national security chief to prioritize religious freedom MORE (R-Va.), Mike Simpson (R-Idaho), Kay GrangerNorvell (Kay) Kay GrangerLobbying world House approves bill increasing federal worker pay House approves 3 billion spending package MORE (R-Texas) and Jo Ann Emerson (R-Mo.) also spoke against the bill.

As expected, Democrats were also quick to pounce on the RSC proposal.

"This is a meat axe approach on top of a meat axe approach," Rep. Norm Dicks (D-Wash.) said, noting that the underlying bill already includes significant cuts. "It's a double meat axe approach."

Rep. Marsha BlackburnMarsha BlackburnThe evolution of Taylor Swift's political activism Kellyanne Conway responds to Taylor Swift criticism by invoking pop star's lyrics Is there internet life after thirty? MORE (R-Tenn.) objected to Lungren's idea that the amendment was a "lazy" approach. "This government is over-spent, we have to get it under control," she said. Several freshman Republicans also spoke in favor of the measure.

Still, many House Republicans have already rejected more than $4 billion in proposed cuts to the spending bill throughout the week, which called into question whether enough Republicans would be able to support Jordan's amendment.

-- This story was updated at 1:30 p.m.