does "open the campaingn" here mean "begin to aruge with ?"
In Booth 13 Youngblood and Roberts opened the campaign with the new President after Kellerman's return to Major Medicine. Roberts told Johnson that he had seen Kennedy's head wound. "The President won't make it," he said. "Let's get out of here."

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In a sense, yes. They are trying to convince him to leave immediately and the author is suggesting that Johnson was initially reluctant.

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It should mean start telling something very surprise or important rather than argue. I did not find any clue of an argument here. However, that's my guess

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