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“That would change my calculus,” Mr. Obama said then.

Mr. Paul thought otherwise.

“I think the line in the sand should be that America gets involved when American interests are threatened,” he said. “I don’t see American interests involved on either side of this Syrian war.”

On the flip side from libertarian-leaning senators like Mr. Paul, GOP Sens. John McCain of Arizona and Lindsey Graham of South Carolina said they cannot support isolated military strikes that are not part of a broader strategy to remove the current regime from power.

Mr. McCain said Sunday that he and Mr. Graham plan to make a trip to the White House on Monday to discuss the administration’s plans.

“We have to have a plan. It has to be a strategy. It can’t just be, in my view, pinprick cruise missiles,” Mr. McCain said on CBS’ “Face the Nation.”

Mr. Kerry, a longtime colleague of both men in the U.S. Senate, says he’s confident that those two — and others — will come around.

“I am convinced that we can find common ground here with them and others so that they’re convinced that the strategy that is in place will, in fact, help the opposition; that there will be additional pressure; and at the same time, that this is not just an isolated pin prick but something that can have a profound impact on Assad’s ability to use these weapons, which he has been using and will use again if we don’t do something about it,” he said on “This Week.”