The latest players to figure in the City Hall speculation game over a possible extension of term limits are none other than Governor Paterson and state lawmakers. Talk is rife that the legislature, at the behest of Mr. Paterson, is preparing to back an effort to extend the city’s term limits for Mayor Bloomberg and the City Council by arguing that restricting public officials from seeking reelection is undemocratic. We can think of another reason they might be interested in seeing the 36 term-limited council members and mayor stay in office for another four years: job security. Several council members ostensibly at the end of their City Hall careers are mounting challenges to incumbent lawmakers in Albany and Mr. Bloomberg, despite protesting that he’s not running for governor, comes out ahead of Mr. Paterson in opinion polls when voters are asked whom they’d like to have as their next governor. Although it may come as a surprise to some that the mayor is signaling a new openness to extending term limits it comes as no surprise that city lawmakers could win support for a term limit extension from the state’s most reliable self-preservationists.