By refusing to exceed to the Congress's wishes that he testify under oath, Karl Rove is testing whether or not the Congress has any guts. He is also banking upon the Federalist Society types unjust so-called justices in the US Judiciary to back him over Congressional rights to oversight.
Frankly, the Congress wouldn't really investigate. They might ask some questions that could be used to impeach Rove's testimony in some other venue if and when some evidence is surfaced showing Rove doing what everyone knows full well he has done, which is political dirty tricks. He's even admitted to it. It's how he got started.
In addition to an extremely weak Congress, there just isn't a powerful independent press anymore with the stomach for going after the story. They don't want to spend the money even though circulation and advertising would rise on account of it if they did it right (the old-fashioned way).
Also, emails and such just have a way of conveniently being lost or overwritten around Rove.
He wasn't supposed to be conducting official Party business from the White House using Republican Party computer servers that could be and were scrubbed to some degree covering tracks. That alone is enough culpability.
, by Ben Evans. The Associated Press. May 13, 2008.