By Manu Raju and Jeremy Herb CNN

(CNN) - Senate Foreign Relations Chairman Bob Corker ramped up his criticism of his Republican colleagues Wednesday, railing on GOP leadership for not wanting to take on President Donald Trump on core Republican issues like trade.

"We're in a strange place. It's becoming a cultish thing, isn't it?" the Tennessee Republican told reporters. "It's not a good place for any party to have a cult-like situation as it relates to a President that happens to be purportedly of the same party."

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Corker's criticism of Republican leaders comes amid his push to get a vote on his amendment to the National Defense Authorization Act that would check the President's ability to impose tariffs.

On Tuesday, Corker gave an animated speech on the Senate floor when he was stymied, saying the GOP colleagues were concerned because "we might poke the bear!"

The dispute spilled into the private Senate Republican lunch Wednesday, where senators engaged in a contentious debate over getting votes on their amendments, including Corker's proposal. GOP senators have pointed fingers at each other for blocking the other's amendments and denying them votes.

Sen. Mike Lee of Utah started it off, raising concerns about lack of votes, before Corker and others chimed in, according to two senators who attended the lunch. Things got so heated that Sen. Lindsey Graham of South Carolina later apologized.

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Corker did not accuse his colleagues of being cultish during the lunch, the senators said.

Corker said Wednesday his comments don't apply to all Republican members, but he said "leadership in general" is not willing to stand up to Trump "because it's all about the next election."

"There's no question that leadership in general is weary of doing anything that might upset the President," Corker said. "It would be unfair to try to say this about every member, that's not appropriate."

Corker argued that if the Senate confronted Trump, it could help bring coherency to the administration's policies.

"To have an administration that wakes up every day on an ad hoc basis just making stuff up as they go along with no coherency to it -- I think us having to weigh in on that would actually cause them to have to think about what they're doing versus, 'Well, I'm upset with X today so I'll do this,'" the Tennessee Republican said.

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But he also pointed to smaller issues, like the Senate Republican plan to work through most of the August recess. Senate GOP leadership has said it's staying in session in August because of Democratic obstruction, but Corker suggested it was to keep Trump happy, who has tweeted that Congress should be working and not leaving town.

"I mean we're going to be here during recess, generally speaking, you know which is fine with me, but it's more about Trump being upset than it is anything else," Corker said.

Corker's criticism of his own party comes as one of the most vocal Republican critics of in the House, Rep. Mark Sanford of South Carolina, was defeated in his primary Tuesday night - with a Trump tweet endorsing his opponent sent the day of the election.

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Many Republicans who have criticized Trump chose to retire rather than run for re-election, including Corker. Arizona Sen. Jeff Flake, another GOP Trump critic who opted to retire in the face of what would have been a difficult primary, said Sanford's loss is another sign that the Republican party is now fully Trump's.

"This is Trump's party. (Former House Speaker John) Boehner said it. We've all felt it. It was reiterated last night," Flake said when asked about Corker's comments. "If you want to win a Republican primary, you can't deviate much from the script. It's the President's script. You can't criticize policy or behavior."

Other Republicans argued that they have pushed back against Trump when appropriate, saying leadership's opposition to Corker's amendment is because the defense bill isn't the appropriate one for the debate Corker is seeking.

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"I have been in a number of meetings with the President, including one last week with 10 senators, where there was a significant give and take, and I think that's exactly what we should want to have happen," said Missouri Sen. Roy Blunt, a member of Republican leadership. "And in the meetings I'm in, that's what does happen,"

One GOP senator suggested that Corker is lashing out because he's upset about his amendment.

"That's the words of somebody who's frustrated because he didn't get an amendment passed," said GOP Sen. Thom Tillis of North Carolina.

Tillis argued it was possible to have disagreements with the President and a good relationship with him, pointing to his legislation that would add protections for special counsel Robert Mueller, which passed the Judiciary Committee but has not come to the floor. "I think the special counsel bill is a good example of where I had a difference of opinion with the President," Tillis said. "I got a great relationship with the President and support the vast majority of everything he's doing."

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Corker's amendment is in response to the steel and aluminum tariffs Trump announced on US allies earlier this month. The measure would roll back the President's trade authority and give Congress the power to check Trump's ability to impose tariffs on national security grounds.

Republican lawmakers have expressed concerns about the Trump administration's tariffs, but they've also been unwilling to embrace Corker's amendment over both procedural issues and broader concerns about undercutting Trump's negotiating position.

In addition to the fight over trade, Corker also brushed aside the President's tweets Wednesday morning declaring that North Korea was "no longer a nuclear threat."

"Well, that would be hyperbole," Corker said.

Corker added that he didn't know if he could trust Trump when he said he'll suspend "war games" with South Korea. "I don't even know, again, if that's real," Corker said. "There's a lot of ad hoc comments that get made that end up not being reality."

Senate Majority Whip John Cornyn also pushed back on Trump's tweets, emphasizing that it's only the start of negotiations with Pyongyang.

"No, I think they made some representations about their intentions but this is the beginning of a long process," Cornyn said. "We are not at the end of the road, we are at the beginning."

But Cornyn doesn't agree with Corker on his amendment. He told reporters last week he supported Corker's amendment, but didn't think "this is a time to pick a fight with the President, in the run-up to a midterm election."

CNN's Ted Barrett and Lauren Fox contributed to this report.

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