The origin of the phrase "off base" or "on base" refers to baseball. If a person is on base, he's right on target or completely has everything in control. If a person is off base, it means that he's caught unaware or unprepared. (If a baseball player is "off base," he can be tagged out, which means a penalty against his team.) However, in the examples you linked to, it implies that President Obama is moving away from the beliefs of his core supporters. For example, if Obama had stated until now that he was in favor of free dental care for all U.S. citizens and was elected by a majority of voters who were also in favor of free dental care, we would say that Obama is moving off base if he suddenly changed his opinion and stated that free dental care is not feasible, and that everyone should pay a fee, even a minimal amount, to get dental treatment.
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