How about @#*$ no. It's called the Great Lakes compact and the Great Lakes Charter. You won't get a drop from us. Nor will you get anything from the mid-west basin.
It's not our problem you built a city in a desert and didn't manage the water properly. You created the problem. Now deal with it. Get rid of the lawns, stop growing crops that need more water than the environment can provide sustainably, build better mass transit to cut back on pollution, stop expanding outward, retrofit existing infrastructure (mandatory water conserving shower heads...make it illegal to sell any that aren't and make it illegal to ship them to california and attach a big fine to companies that do, turn off park fountains, recycle wastewater back into the aquifer, etc), etc. There's plenty you can do now to stop the problem.
Bottom line. You won't get a drop from the great lakes. The residents here surrounding the great lakes will tell you to take a hike.