well technically the secretary of state Doug la follette has to publish it. It can be done online and is typically done by the reference bureau within 10 working days after it is signed.
I also found this: Governor must sign or veto legislation within 6 business days after transmittal, or it becomes law without signature.
Here: http://www.statescape.com/resources/governors/govsigndeadline.aspx
So we are getting much closer...