Speaker as head of government and president as head of state? Thoughts?

Before certain reforms in the early 1900's, the Speakers of the House wielded a lot more power than they do today. Could it be possible for a cunning Speaker - say, Reed - to slowly strip the President of his powers and have the Speaker of the House as de facto head of government, in a sort of parliamentary system? The President would be nothing more than a figurehead, much like the British queen is today. Is this feasible? If so, how to go about doing it?
 
But probable before TR became POTUS. Future speculation predicted this until he got there.

Indeed - Reed was enormously powerful on the American political scene, probably more so than anyone else in the government. However, his lack of charisma might impede this.
 
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