Not as strong as you might expect......at least as it applies to the Ohio primary.......considering his Administration is generally considered both successful and comparatively popular.
Kasich is obviously quite a bit higher up the food chain here than in recent Primary states. However, he isn't any kind of favorite at this point; I think Trump is generally thought to have a modest lead of maybe 5-8 points with JK in second place. He's obviously thrown all his eggs into the Ohio basket.....and I suppose he can win if everything goes right......but I honestly wouldn't bet too much money on it..
Cruz likely won't show very well statewide in light of the fact Ohio's is an open primary. I suspect he'll have solid support in populated suburban SW Ohio outside the city of Cincinnati.....that's where I live......which is almost exclusively blood red Right-wing. But I also suspect moderates around the State.....especially Dems (like myself) who have little, if any, interest in voting for Hillary or Sanders.....will be taking a Republican ballot and choosing between Kasich and Trump.
Speaking only for myself, I'd love to see Cruz get his doors blown off and run a poor 4th. But Rubio isn't trying here, and has largely yielded the establishment to Kasich. So, I suspect Cruz will finish 3rd; though how well he runs remains to be seen.