Where, in the excerpts discussed here, did the Vice President of the United States say that the President has the right "to dissolve the Constitution"? Cheney gave a general answer to a vague question and pointed out the obvious fact that the President does not have to consult Congress before launching nuclear weapons--mostly because in a launch situation, there would be no time for such consultation. That's it. Nowhere did Cheney discuss anything about the President having the power to dissolve the Constitution and nothing the Vice President said could even plausibly be interpreted as advancing that proposition.
I realize that Andrew Sullivan doesn't like the Bush Administration. That doesn't give him license to make things up on his blog. Blatant and shameless dishonesty is unbecoming, after all.