Where is it that you see the Constitution grants any authority for the Speaker of the House to nullify these?
It's in the same section where it gives the president the authority to change the meaning of the 2nd Ammendment.
“...Lemme try it this way...”
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If you think it would be a good thing
for the Speaker of The House to act outside of the Constitution
in response to the President acting outside of the Constitution,
then I have to disagree with you.