Just to confirm what Max has said:
Class action lawsuit against SAFE Act | WIVB.com. There is a 2:32 minute news clip on this page.
The suit is filed. Since part of the Act engages on April 15 and the next court date is April 25th, it is natural to ask for an injunction. And since the suit is filed, it can now become a class action suit. Demanding a Jury trial puts the onus on the common people rather than a judge, to determine the constitutionality of the law.
Added to this that there are some small political consequences in being a sitting Governor being called to the witness stand and defending your own law... Remembering that Cuomo is on record as saying that he won't be taking New Yorkers' guns... Can't imagine how that one will play in front of a jury!