On a biological level, there'd be no problem providing a vegetarian diet for everyone. A healthful vegetarian diet is not hard to achieve, at least no harder than a healthful non-vegetarian diet.

From an infrastructure point of view, providing everyone vegetarian food sources overnight would not be possible, but that's not a realistic scenario. With a gradual transition, the transition would reduce overall resource use on basically all fronts, so there's no reason to expect extraordinary problems.

Of course, this is all theoretical unless people care enough to change their lifestyles.