The amendment in question is a bipartisan proposal offered by Corker and 13 other senators last week that would allow the Senate to accept or reject tariffs when the president puts them in place as a matter of national security.
Corker's portrayal of his colleagues' support for Trump as "cult-ish" has bothered Graham and other senators.
Though GOP lawmakers have publicly fretted over Trump's tariff policies, GOP leadership has shown little interest in formally pushing back against the president.
"I haven't heard a single senator on our side that hasn't expressed concern to the president directly about what's happening with tariffs", said Corker said from the Senate floor late Tuesday.
Sounding exasperated, Corker said Republican senators overwhelmingly agree with the concept behind his bill, but are afraid of upsetting the president.
Inhofe said inclusion of the amendment would jeopardize passage of the defense bill or delay its passage.
Graham launched into an expletive-laced attack on Corker during the lunch as their colleagues looked on, people familiar with the discussion said.
Las primeras fotografías de 'Wonder Woman 1984'
Esta última tiene previsto su estreno en España para el 13 de julio de 2018. Detrás de cámaras, Patty Jenkins regresa para dirigir Wonder Woman 1984 .
"Canadians, we're polite, we're reasonable, but we also will not be pushed around", said Canadian Prime Minister Justin Trudeau. The people describing the lunch spoke on the condition of anonymity to talk more candidly about a private gathering.
Representatives for the senators did not comment on the details of the lunch.
"Well, that would be hyperbole", Corker said. Lee responded. "That is one of the most uncollegial and inappropriate arguments I've ever heard, and I will not tolerate that". Trump returned the insult by suggesting on Twitter that Corker wouldn't even be able to get elected dog catcher in Tennessee and giving him the nickname "Liddle Bob Corker".
Tur pressed him on the idea that so many Republicans are too anxious to speak out against Trump on anything lest they incur his "wrath", bringing up Mark Sanford's primary loss last night as an example.
The tense lunch underscored another long-simmering irritation in the Senate this year: a legislative chamber that had yet to do much legislating, with few votes on amendments taken so far this year. "The president might get upset with us as United States senators".
"We are so strong in the automotive industry, I am anxious about the impact particularly on our suppliers", said the governor. He just kept walking.