If Romney doesn't carry Michigan, he's toast.
I doubt Mittens will carry Michigan, and I doubt he would be toast when he doesn't (particularly if he carries AZ while losing Michigan), so your hypothesis may well be tested.
MI and OH are not good places for Mitt. MI is kind of horrible for Mittens when you think about it. They may like Santorum's GATT breaking manufacturing industrial policy which is sort of a proxy appealing to those with protectionist impulses (Mittens is more laissez faire), and the Pubs are quite Catholic and Dutch, both groups with which Rick should do quite well. He's been sweeping the Dutch everywhere so far (check out the results in Marion, Sioux and Lyon Counties in Iowa). OH isn't much better. It's light on the Dutch, but has the Butternut region, and a fair number of Mennonites, along with the Catholics. Mittens' path to the nomination will need to come from the NE, the West, and more practical and hardbitten and less ideological places like Indiana and Illinois (with lots of higher income suburban white collar voters). Mittens is fortunate that the way delegates are awarded is skewed heavily in his favor overall.