Christine Quinn made a move to shore up her own political future yesterday when she urged New Yorkers to support a change in New York’s term-limit rules. The announcement was made after Mayor Bloomberg’s proclamation that he’d seek a third term. It’s pretty much the opposite of what she’s said before — and Quinn conceded that she’s had a “change in [her] position.” Though it was a flip-flop, the move was anticipated on her part because Quinn has her own mayoral ambitions. Unlike her fellow Democratic aspirants, like Comptroller Bill Thompson, she is likely to benefit from another four years in the wings. A change in term limits will mean she’s able to run for City Council speaker again, and therefore put even more time between herself and the slush-fund scandal that scarred her reputation earlier this year. Now it’s up to Quinn to bring the necessary Council votes to change the limits rule. If not, as Elizabeth Benjamin pointed out, her position could be weakened to the extent that a mayoral run next year might be out of the question for herself. Looks like the players on Wall Street aren’t the only high-stakes gamblers downtown this week.