The Governor cannot order AG Lisa Madigan to do anything, she is an elected official and in Illinois is not required to do what the Governor desires. If he vetoes the bill, the senate and house will go into special session and override his veto with the original language, the huge majorities in the house and senate assure that. There will be no appeal or stay. Quinn will either sign it or ammendatory veto it before the 9th, depends which he feels will play better in his re-election campaign. Either way he is just a speed bump in the road at this point. Speaker Madigan will not let this touch his daughter and President Cullerton is already on board too. Too many legislators afraid of going off the court carry cliff to change anything now. Negotiations are done, the bill passed with over 75% support in both houses, only 60% was required for preemption and only 60% is required to override the governor's veto and pass the original bills into law. The last time Quinn tried an ammendatory veto on a gun bill he got stuffed by larger majorities than supported the bills in the first place.
The only thing Quinn could do to stall at this point is to try to wait the 60 days he has to sign or veto the bill and then let it become law without his signature or veto it then. However, I see no upside for him in that case, he has caused a crisis that did not need to happen by refusing to act. It would hurt him with both democrats and republicans.
Lisa might ask for a temporary injunction then with the 7th then, "because our governor is an idiot," or she just might let him fall on the sword of his self created crisis. He would be crucified in the press.
So he either signs or vetoes and gets overridden. Either way he is irrelevant at this point, except the legislators would all be ****** if they have to come back in special session for an override vote.