@rugbygirl - I guess one reason might be if the president was lukewarm about the bill. You know, didn't want to veto or maybe didn't have the political capital to veto. (If a presidential veto gets overridden, he looks like kind of a loser!)
Or maybe the president supports the general idea, but finds it flawed. One case I've read of where this happened was when Congress passed a law outlawing flag burning during the George H.W. Bush administration. President Bush supported banning the burning of the flag, but he thought a constitutional amendment would be the better course.
He was right, of course. The Supreme Court struck down the law as being unconstitutional (which it was - violates the first amendment) and as far as I know, the idea of a constitutional amendment has never gained much traction.