First, regardless of whether any of this sounds true and regardless of whether such a tap would require a judicial finding of probable cause against the target, there's a much bigger problem: Congressional investigations such as these are almost entirely a matter of Congress ferreting out and examining things that happened within the executive branch. To use a clumsy but helpful analogy, this kind investigation means having the folks in Congress's house find out what's in the President's house. But the President is in the President's house. He doesn't need to investigate. He knows. He's in the house! He owns the house!
Now, one might speculate that the executive branch is so vast and sprawling that the President somehow needs Congress to come in and figure out what's going on. But here the President has already kneecapped himself. Here's why.
The President says this happened. He says he has the evidence. He knows it happened. If he knows it happened, there's nothing to investigate. The President has plenary power to declassify and publicize anything he wants. Anything. He can do it by the book or he can do it basically by fiat with no one involved at all.
My best guess is that is a typically Trumpian development in that it involves both abject lying and a big splat of ignorance, laziness and ridiculousness of simply having no idea of how the different branches connect with each other. He hasn't realized that demanding a congressional investigation is different when you're President rather than some old guy getting angry watching Fox News in the living room. The President is in essence demanding Congress investigate him. Yes, he thinks it's Obama. But he inherited Obama's house. Whatever Obama did, Trump owns it.