Um, Edward's answer was stupid, because it's exactly the opposite of that. Actually, it's an old cliche, and Reagan wasn't the first to say it. Simply put, it's you stick with what got you to where you are in the first place. It's kind of a dumb concept, because it can also mean sticking with a policy that's no longer relevant to current circumstances just because it was one that was successful under the old set of circumstances. A good example would be US policy toward Cuba. Under the circumstances that existed in the 1960's where Cuba was a military threat to the US, a strong arm military posture was essential to protect our interests. Now that Cuba is no longer the threat it used to be, "the one who brung ya" (i.e. the military posture) makes less and less sense. Those who are hawks toward Cuba are "dancing with the one who brung them" despite the fact that that approach no longer yields results.
To Edward's point, however, it's funny that Reagan apparently didn't follow his own advice. He didn't dance with the one that brung him when he divorced Jane Wyman to marry Nancy Davis or when he switched parties from Democrat to Republican early on in his career.