Is the end of April too late to find placement in Ph.D programs in the U.S.?
For the most part, yes, it is too late to be considered for graduate admissions at most programs for this coming fall, as most schools have already made their decisions as to who they will admit. 

That said, if you are an exceptionally qualified candidate, and unusual circumstances have taken place, it may be possible to be considered by specific programs. However, there has to be some really strange events taking place. (For instance, one school I know had a banquet during their one prospective students' weekend, and accidentally food poisoned everybody—and ended up with 20% of their expected yield of students. They probably would have loved additional late applicants!)

But, basically, you'd need a department that had a major shortfall of accepted students compared to their research needs, and you'd need to be a candidate that would be strong enough to accept in the regular admissions cycle.