How many amendments? As many as are needed.
Every American citizen does NOT have the CONSTITUTIONAL RIGHT to vote.
Most citizens have the
privilege of voting
PROVIDED that they have jumped through the administrative hoops that have been established by ordinary legislation. And, ordinary legislation can be changed without any constitutional change and it would be perfectly "constitutional" (but rather stupid) to deny anyone with blue eyes the ability to vote.
In Canada EVERY citizen DOES have the CONSTITUTIONAL RIGHT to vote. True, they do have to establish their identity before they can get a ballot that will be deposited in the regular ballot box and counted along with the other regularly cast ballots but that does not detract from the fact that they do have the CONSTITUTIONAL RIGHT to vote. (For examples of the incredibly restrictive criteria for proving your identity in order to vote in Canada see
HERE.)
Now where you got that I'd "push to scrap an entire constitution for that" I simply have no idea. Face it, they didn't have to "scrap an entire constitution" in order for those who were formerly slaves to vote and they didn't have to "scrap an entire constitution" in order for those who were female to vote, and they didn't have to "scrap an entire constitution" for those over the age of 18 to vote.