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 FrelinghuysenElection Countdown: Florida Senate fight resumes after hurricane | Cruz softens ObamaCare attacks | GOP worries Trump will lose suburban women | Latest Senate polls | Rep. Dave Brat gets Trump's 'total endorsement' | Dem candidates raise record B Trump to fundraise for GOP candidate in key NJ House race Florida politics play into disaster relief debate MORE (R-N.J.), Frank WolfFrank Rudolph WolfVulnerable Republican keeps focus as Democrats highlight Trump Bolton could be the first national security chief to prioritize religious freedom House votes to mandate sexual harassment training for members and staff MORE (R-Va.), Mike Simpson (R-Idaho), Kay GrangerNorvell (Kay) Kay GrangerThe stakes are sky-high for the pro-life cause in the upcoming midterms Bipartisanship alive and well, protecting critical infrastructure McCarthy's path to Speaker gets more complicated 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 BlackburnKaty Perry praises Taylor Swift for diving into politics Celebrity endorsements aren't kingmakers, but they may be tiebreakers Election Countdown: Florida Senate fight resumes after hurricane | Cruz softens ObamaCare attacks | GOP worries Trump will lose suburban women | Latest Senate polls | Rep. Dave Brat gets Trump's 'total endorsement' | Dem candidates raise record B 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.