MAKING THE CASE…. Lawrence Eagleburger, deputy secretary of State under Bush I, has been a McCain campaign advisor and occasional surrogate for nearly a year. As it happens, once in a while, Eagleburger strays from the script — and that’s not a good thing for McCain.

In March, for example, Eagleburger appeared at an event in DC, where he described the GOP’s religious right base as “a serious problem” that he wants to see Republicans fight “hard against.”

Yesterday, Eagleburger appeared on NPR as part of a segment on “making the case” for a McCain presidency. His candor was welcome, but not by McCain campaign headquarters.

A former Republican Secretary of State and one of John McCain’s most prominent supporters offered a stunningly frank and remarkably bleak assessment of Sarah Palin’s capacity to handle the presidency should such a scenario arise.

Lawrence Eagleburger, who served as Secretary of State under George H.W. Bush and whose endorsement is often trumpeted by McCain, said on Thursday that the Alaska governor is not only unprepared to take over the job on a moment’s notice but, even after some time in office, would only amount to an “adequate” commander in chief.

“And I devoutly hope that [she] would never be tested,” he added for good measure — referring both to Palin’s policy dexterity and the idea of McCain not making it through his time in office.

The NPR host went on to ask if Palin could step in during a time of crisis. “It is a very good question,” Eagleburger said. He paused, laughed, and added, “I’m being facetious here. Look, of course not.”

Just to add to the entertainment, Eagleburger added, “Give her some time in the office and I think the answer would be, she will be [pause] adequate. I can’t say that she would be a genius in the job. But I think she would be enough to get us through a four year… well I hope not… get us through whatever period of time was necessary. And I devoutly hope that it would never be tested.”

Keep in mind, Eagleburger is not just some random McCain supporter. McCain touts Eagleburger’s endorsement all the time, and the campaign sent Eagleburger to NPR to emphasize why voters should support the Republican ticket.

Last week, McCain chatted with Don Imus, and expressed frustration about Republicans who’ve questioned Palin’s qualifications. “What’s their problem?” McCain asked. “I think she is the most qualified of any that has run recently for vice president.”

Just days before the election, McCain hasn’t even convinced his own advisors of this.

Nor has he made the case to voters: a new New York Times/CBS News poll found 59% of Americans consider Palin unprepared for national office. The report added, “The increase in the number of voters who said Ms. Palin was not prepared was driven almost entirely by Republicans and independents.”

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Follow Steve on Twitter @stevebenen. Steve Benen is a producer at MSNBC's The Rachel Maddow Show. He was the principal contributor to the Washington Monthly's Political Animal blog from August 2008 until January 2012.