Mr. Binder said a unified majority would counterbalance the county executive and the minority caucus, providing "a vocal opposition when appropriate."
Most members of the minority caucus are Democrats, so their opposition would not end Mr. Verniero's chances in the Senate, where Republicans hold a 24-16 advantage.
Friedman and the minority caucuses had opposed the name change.
He points out that some members of the minority caucus, like Archie Spigner of Queens, share his views.
"It would appear to me that the Democratic leadership thinks that the minority caucus is much more powerful than the Jewish constituency," she said.
Although the caucus was re-formed after the 2001 elections, some Council members say privately it is ineffective, unlike the minority caucus.
Members of the Council's minority caucus criticized the bill sharply in recent weeks, noting that lead poisoning overwhelmingly effects minority children.
But to members of the Legislature's minority caucus, it may also illustrate their growing clout in Albany.
All but seven are Democrats in the Assembly, making a united minority caucus a potentially formidible force within the 150-member lower house.
The leader of the minority caucus is called either the Republican Leader or Democratic Leader, depending on which party is in the minority.