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 FrelinghuysenConservative lawmakers met to discuss GOP chairman’s ouster Overnight Finance: GOP delays work on funding bill amid conservative demands | Senate panel approves Fed nominee Powell | Dodd-Frank rollback advances | WH disputes report Mueller subpoenaed Trump bank records Overnight Finance: House approves motion to go to tax conference — with drama | GOP leaders to consider Dec. 30 spending bill | Justices skeptical of ban on sports betting | Mulvaney won't fire official who sued him MORE (R-N.J.), Frank WolfFrank 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 GrangerSeven Texas lawmakers leaving Congress means a younger, more diverse delegation House passes .5 billion disaster relief package GOP lawmaker: No town halls because of threats against lawmakers 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 BlackburnFormer Dem Tenn. gov to launch Senate bid: report Google, Facebook and Drudge: What the new titans of media mean for America Learning from the states: Feds should adopt anti-pyramid scheme law 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.