Bears are bluffing. No way they move to Northwest Indiana if there's even a possibility of the Arlington Heights site working out. Reason is in Arlington Heights, IL (disclaimer: where I have an aunt and uncle living) they actually have more room to build an entertainment district than at the proposed site in Hammond, IN. So in the longer run, they make more money in Arlington Heights than in Hammond. Yes $2 billion in free money from Indiana is nice, but nice enough to counteract that? Probably not over decades and decades.
Plus I'm not sure I can describe in words just how much people in Chicago look down on Northwest Indiana. Would be a huge psychological issue for Bears fans. This guy Warren who the Bears hired to negotiate their stadium deal, he's just a businessman looking for the best deal but the Halas family is Chicagoans and they likely get the same ick that any Chicagoan does over Northwest Indiana.
Bears are trying to squeeze out a few extra concessions from the Illinois legislature or create urgency to get an Arlington Heights deal fast-tracked. I'm not sure I would play along if I was Illinois: they can't beat the Indiana offer on dollars and cents and state finances are not so great. Call the bluff, that's their strongest move.