Michele Bachmann and Ron Paul want Congress to be able to challenge - and thus influence - Federal Reserve policy. This would be a disaster. Fed Chairs have to deal with the complex reality of a modern economy; members of congress, by contrast, need to worry only about whether their ideology aligns with most voters in their district. For this reason it is easier to trust - even if harder to understand - a Fed Chair than a Congressperson.
It's possible that members of congress have incredibly simple models of economic reality; it's also possible that they just think their constituents have such simple mental models. In either case, they seem to focus on the simplicity of principles rather than the complexity of reality, focused on ideology while relegating reality to their peripheral vision.
20th century politics in the West is pretty simple to understand. At the one extreme are communists who don't trust traditional capital markets and at the other extreme are robber barons who don’t trust any regulations on markets. Few in the West believe in such extremes now, but everyone leans one way or another. One question that determines whether you become a conservative or liberal is, How much - if at all - do you think governments should intervene in capital markets to do what is best for labor markets?
Which brings us to Keynes. He did not take a stand along this spectrum between extremes. Instead, he said that the right policy depends on economic conditions. Fed Chairs - our central bankers - have generally continued in his tradition; by contrast, members of congress seem convinced that it's more important to avoid nuance and take a stand instead, proving that you have principles by never changing your stated reliance on either markets or intervention.
Keynes' signature work - the one that essentially invented macroeconomics - he titled General Theory of Employment, Interest and Money. I'd suggest that the title could have been General Equilibrium because a large part of his theory rests on the notion that capital markets can reach equilibrium before labor markets do. Simply put, investors might rationally choose to stop investing in industrial capital and new businesses before everyone looking for a job has one. What is optimal for capital markets may be sub-optimal for the economy as a whole. His interest was not in the equilibrium of capital markets but a more general equilibrium that included labor and capital markets.
Keynes generally trusted capital markets (he got rich by starting his day in bed reading stock reports and issuing trades before getting on with his day), but also knew that their interests weren't perfectly coincident with labor markets. He argued that capital markets can - for extended periods - reach an equilibrium that isn't good for the economy. (The Great Depression that resulted in 25% unemployment caused a lot of people to agree with him.) If investors don't see good business prospects, they will hold off on investments. If they hold off on investments, jobs won't be created. If jobs aren't created, consumers buy less. If consumers buy less, investors won't see good business prospects. When that happens, Keynes said, good policy would increase demand through fiscal policy (some combination of additional spending and tax cuts) and monetary policy (making money cheaper by lowering interest rates, thus encouraging borrowing and spending). Fiscal policy is the job of Congress. Monetary policy is the job of the Fed. (Oh, and when unemployment is low and inflation is high, Keynes would suggest tax hikes, lowering spending, and / or tighter monetary policy, reversing the policy needed for dealing with unemployment. Good policy depends. Bigger or smaller government? Depends. Higher or lower taxes? Depends.)
Fed Chairs are pretty consistently Keynesian, choosing to deal with inflation with tight monetary policy (as Volker did in the late 70s and early 80s) and unemployment with loose monetary policy (as Bernanke has done more recently). There are differences of opinion about tweaking policy in between the extremes of 10% unemployment and 18% inflation but no Fed Chair doubts that the answer is, "It depends." In that sense, Fed Chairs are all Keynesians now.
Members of congress, by contrast, seem to reject such nuance. While Yellen tries to focus on economic realities, glossing over ideological differences, congress instead focuses on ideology and glosses over the complexity of reality. And while there are exceptions to this broad brush characterization within Congress, Michele Bachmann and Ron Paul are not these exceptions.
As you listen to the questions Congress asks Yellen (and in many cases they don't ask questions but instead do little ideological advertisements before asking her to affirm their beliefs), it is pretty simple to decode. Republicans ask about the impact of Fed policy on capital markets and the threat of debt and inflation. Democrats ask about the impact of Fed policy on labor markets and the threat of unemployment. Republicans are never quite convinced that the Fed is doing enough to reduce debt or fight inflation. They worry that policy will erode returns to capital with inflation or low interest rates. Democrats are never quite convinced that the Fed is doing enough to reduce unemployment or to make money looser, thus lowering unemployment rates for the nation's poorest.
Janet Yellen, fortunately, is drawing from a broad array of data, more interested in general equilibrium. She's dealing with investors who can be spooked, people looking for work who can be discouraged, and currency exchange traders who will literally turn on a dime from buyers to sellers of the dollar. She has to consider a number of variables when formulating policy. Yellen feels responsible for moving towards a general equilibrium; Many members of Congress, by contrast, appear responsible only for proving their ideology. (And that might be the simplest reason their approval rating has only recently risen out of the single-digits.)
Ideology makes it easy to win elections but hard to formulate economic policy. To turn Fed policy over to Congress would be like buying a car that only turned right or left rather than one that could be steered in either direction depending on the curve of the road ahead. And that kind of car is guaranteed to crash.