Good point, but the President does not need to respond to Cruz’s introduction of the legislation or the amendment. The Senate would not even need to call a vote on it.
But the news of its introduction could, like the news of FDR’s proposal, cause the judiciary to back down.
But the context was different.
FDR’s proposal to pack the court was not shot down, it was withdrawn by FDR because he got what he wanted which was the SCOTUS siding with him on his New Deal programs.