The president, through the attorney general (28 CFR 600). Congress can make a bunch of noise, which might spook the president into action. It did so to get an independent investigation of the "who leaked that Plame worked for the CIA?" question.
Congress can and does perform its own independent investigations. It doesn't need to have an outsider to perform its work. The advantage to having the executive branch involved is that the executive branch can bring criminal charges, while Congress can't. But, Congress has the power to remove officials from office.
Expecting Congress to do anything about this, other than flap its gums, runs counter to all of recent history.
In essence, NADT will happen.