WASHINGTON — A spokesperson for Sen. Tommy Tuberville sparked a backlash Thursday from Republicans after privately floating primary challengers for senators who vote to end-run Tuberville’s blockade of military promotions.

The uproar comes as Republicans are making their frustrations with Tuberville’s monthslong hold on more than 300 high-level military promotions increasingly public. In a four-and-a-half-hour floor fight on Wednesday night, several Senate Republicans tried to pass 60 military nominees individually, with Tuberville objecting to each.

On Thursday, the Alabama Republican confirmed that regardless of his colleagues’ objections, he plans to continue his hold on nominations until the Pentagon changes its abortion policy. But he quickly distanced himself from his aide’s remarks as one top Republican said the staffer should be punished.

The spokesperson, Steven Stafford, asked anti-abortion groups in an email last Thursday to publicly oppose Senate Republicans who back a Democratic effort for a one-time suspension of the rules to circumvent Tuberville’s blockade.

“In my opinion it is imperative for all of the groups to make clear, in some words, that any Republican who votes for this will be primaried,” Stafford said in the email, which was first reported by Politico and confirmed by NBC News.

But some Republican senators were furious.

“I have seen it. I have some words and they’re not polite so I’m not going to say them,” said Sen. Joni Ernst of Iowa, who was among a group of Republicans that confronted Tuberville for his tactics Wednesday on the Senate floor.

Sen. Steve Daines of Montana, the chair of the Senate Republican campaign arm, which is tasked with protecting incumbents, said the staffer should face some punishment, “up to and including termination.”

“My understanding is it did not come from Senator Tuberville, it came from his staffer, and I’m confident that Senator Tuberville will take appropriate action,” Daines said. “It’s a violation of ethics rules, and it needs to be dealt with severely.”

Asked to comment, Stafford said his boss wasn’t aware of the email.

Tuberville told NBC News: “That was not me. That came from in my office on some memorandum. Definitely against that.”

“These are my teammates,” he said, referring to GOP colleagues. “I mean, this is getting way out of proportion when it comes to that. We all disagree, right, in some form or fashion. But no, I had nothing to do with that. First time I saw it was yesterday.”

Still, Tuberville himself had warned Wednesday that it would be “suicide” for Republicans who vote for the rules change.

“They’ve got to vote for their constituents, they don’t vote for themselves,” he said. “See, I don’t understand that, I mean, you’re either pro-life or you’re not, and so if they vote against this it’s going to be suicide for some of them. Let them do it.”

The Senate can still take up military nominations while Tuberville’s holds continue; his blockade just dramatically slows down the process. Democrats have largely dismissed calls to do the confirmation votes one by one, saying it is untenable and they should be done in batches as is normal practice.

The Senate voted to confirm the promotions of three top-level military officials on Thursday afternoon in the face of Tuberville’s holds. They are: Adm. Lisa Franchetti, the new chief of Naval Operations; Gen. David Allvin as chief of staff of the Air Force; and Lt. Gen. Christopher Mahoney, who was confirmed as assistant commandant of the Marine Corps. Mahoney’s confirmation comes as the commandant of the Marine Corps, Gen. Eric Smith, has been hospitalized since having a heart attack over the weekend.

Sen. Richard Blumenthal, D-Conn., one of the Democrats leading a resolution to bypass Tuberville’s holds, said Wednesday that Smith’s hospitalization “simply illustrates very dramatically the personal consequences of this unconscionable hold,” noting that because Smith was without an assistant commandant he was “working, as reported, 18 hours a day or more doing two highly critical jobs under tremendous pressure.”

“That’s not only bad for his health but also for our national security. … I hope it will clarify in my Republican colleagues’ minds the toll that this hold is taking. It’s not just conceptual or hypothetical, it’s real in the lives of our military, and it’s not just the nominees who are affected, it’s the entire command structure,” Blumenthal continued.

Sen. Jack Reed, D-R.I., who chairs the Armed Services Committee, said he’d defer to Smith’s doctors, but echoed Blumenthal’s concern.

“It just illustrates the fact that you’re doing two significant jobs simultaneously and working hours that the commandant was working — five in the morning until 11:30 at night — will have an effect on most people,” he said. “I know it would have an effect on myself and most of my colleagues, and probably a serious one.”