Plausibility: Possible US Parliament?

I think its easy to make an american Parliament System if you go back and change the Constitution, but is it possible that the Republican Congress abolishes or signifigantly weakens the Executive Branch during the Johnson Administration, and makes an American Parliament?
 
I think the notion of the Johnson administration is kind of on target. Essentially, in the middle of the 19th century most American Presidents were pretty weak by modern standards (Lincoln is the major exception).

If Congress started impeaching presidents fairly often, then I could see, over time, the head of one of the branches of Congress becoming dominant... the only question is, how do you decide between the Speaker of the House and the Senate Majority Leader?

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Bill
 
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