It is a set of rules and conditions under which "we the people of the United States of America" agree to be governed to preserve "certain unalienable rights" that are referred to in the Declaration of Independence. The obligations of this relationship are all on the government, not on the governed. So there is no contract to declare null and void, and even if there were, there is no instrument to do so other than We the People taking action to reclaim our unalienable rights, which would be indistinguishable from actions in the absence of a contract.
These actions are limited and consequential, and the outcomes of such actions are unpredictable.
One is We the People deciding to overthrow current government, peacefully or violently. Another is the action which you preclude in the OP: the two branches of government, Legislative and/or Judiciary, checking the Executive branch and restoring it to its intended function on behalf of We the People. The third is for We the People to petition the government to hold unscheduled elections, but this will have to be done through the branches of government you stipulate to be dysfunctional and incapable of living up to their obligations. The fourth is non-intervention by We the People, in hopes of the government to eventually heal itself. The fifth is maintaining the status quo and awaiting an opportune moment to implement any of the options listed above. The sixth is anarchy: ignoring the government altogether.
None of these seem particularly appealing to me. So I am not offering a solution to a current situation, only attempting to address a hypothetical you posed.
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