Let's look at Article V of the Constitution, shall we?
The Congress, whenever two thirds of both Houses shall deem it necessary, shall propose Amendments to this Constitution, or, on the Application of the Legislatures of two thirds of the several States, shall call a Convention for proposing Amendments, which, in either Case, shall be valid to all Intents and Purposes, as Part of this Constitution, when ratified by the Legislatures of three fourths of the several States or by Conventions in three fourths thereof, as the one or the other Mode of Ratification may be proposed by the Congress; Provided that no Amendment which may be made prior to the Year One thousand eight hundred and eight shall in any Manner affect the first and fourth Clauses in the Ninth Section of the first Article; and that no State, without its Consent, shall be deprived of its equal Suffrage in the Senate.
This says, Defiant6, that EITHER the U.S. Congress (both Houses), whenever two-thirds of each decide; or two-thirds of the Legislatures of the States APPLY (whatever the hell THAT means), shall call a Convention....
....wait for it...
...FOR PROPOSING AMENDMENTS.
Ain't nothing in there about putting the whole Constitution up for grabs.
Did I miss something somewhere? I'm not at all sure where you get that business of an Article V Convention (which is its proper term, btw, as the only Constitutional Convention we ever had was back in the day) puts the entire Constitution on the proverbial chopping block.
Furthermore,
Hollingsworth v. Virginia (1798) and the Supreme Court Decision that came out of it, makes the case that the President does not have the power to veto a constitutional amendment.