A short piece at dcexaminer.com takes a look at the history and current state of maverick. Usually pieces like this are eager to provide an easy story that sounds reasonable. And they're often much too easy to be true. Those are called folk etymologies.†
But this story keeps it together and gives a decent history.
In the 1860s, Samuel Maverick was an indifferent herder who refused to brand his cattle. When cowboys would see his unmarked cows wondering the countryside, they'd say, 'Oh that's a Maverick.'
Compare that to the OED entry:
< the name of Samuel Augustus Maverick (1803-70), U.S. politician, and the owner of a large herd of cattle in Texas in which the calves were unbranded.
Also relevant to the story of this word: the use of an emerging derivation
It seems the family's biggest confusion is not that McCain links himself to a liberal family (We have some Republicans in the family nowadmits Mrs. Maverick) but that he hasn't done anything verymavericky.
Mavericky is an adjective that is formed by the derivational adjective suffix -y. It's been making the rounds. SNL used it amusingly in its VP debate sketch
Tina Fey (as Sarah Palin): With Barack Obama you're gonna be payin' higher taxes. But not with me and my fellow maverick. We are not afraid to get mavericky in there and ruffle feathers, and not got to allow that. And also too: the great Ronald Reagan.
† We could say a lot about the different types of folk etymology. Two major types: 1) Explicit: a false story about the history of a word. Explanations like the claim that posh is an acronym for Portside Out Starboard Home; or that fuck is an acronym meaning for unlawful carnal knowledge or fornication under carnal knowledge or fornication under command of the king; or that hooker (prostitute) is related in origin to Civil War general Joseph Hooker —all false. 2) Effective: a morphological analysis that mistakenly connects words just because they sound or look similar. These might not be explicitly noted but they often affect pronunciation (as Geoff Nunberg suggests that a folk etymological connection to words like molecular and particular has effected the pronunciation 'nuk-yu-ler') or meaning (as jejune has been connected to the idea of youth probably because of resemblance to juvenile while the true etymology connects it to the sense of emptiness by fasting).