No doubt that things have gone down hill since the New Deal. But our congressional reps are still susceptible to (and can do something about) local pressure from their constituents.
I'm skeptical. The beltway bureaucracy is a natural constituent of Democrats and their big-government social engineering ideas. They're well entrenched and well versed in the ways of Washington and can sandbag a investigation into oblivion if they want to, particularly if they get a little help from their liberal/Democratic allies in the legislature. The deck is heavily stacked against any conservative investigation of the actions, policies, and agenda of the bureaucracy.