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 FrelinghuysenWeek ahead in defense: Spending bill, Yemen vote top agenda Top appropriations Dem: Omnibus talks 'locked down' Spending talks face new pressure MORE (R-N.J.), Frank WolfFrank Rudolph WolfHouse votes to mandate sexual harassment training for members and staff Trump, global religious freedom needs US ambassador to lead Bottom Line MORE (R-Va.), Mike Simpson (R-Idaho), Kay GrangerNorvell (Kay) Kay GrangerTrump gives jolt to push for military ‘space force’ Overnight Defense: Pompeo brings hawkish Iran stance to State | Air Force ducks on 'space force' | Senate eyes vote on US role in Yemen war | Perry doesn't want to be VA chief Air Force leaders sidestep question on Trump's 'space force' 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 BlackburnThree states where Dems can pick up Senate seats Ex-Tennessee gov's Senate campaign notifies FBI of potential hack Overnight Regulation: White House says Trump still opposes elephant trophies despite new policy | SEC wants crypto exchanges to register | GOP senator offers net neutrality bill | Biofuel pushes Trump to preserve ethanol mandate 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.