The proposal and many like it miss the whole point of the Bill of Rights and why it exists and what it was meant for. The Bill of Rights was designed to protect rights that were not popular. Jefferson and the others involved didn't enshrine the rights to the press, assembly, and the criminal rights because they were a codification of what would be popular and accepted. The Bill of Rights was enacted to protect rights that might not stand up to the democratic process. By adding the rights to the Constitution they were assuring that they would be a part of our democracy even if they could not pass a popular vote. The rights are protected even if they are unpopular. The classic example is the right to free speech. For many the right to speech could be popularly protected. But for many (the Nazis come to mind) the right would not survive the democratic process.
The process to establish rights under the Constitution is exactly the same. Brown v The Board of Ed. was not popular but in that case the Supreme Court held that separate but equal was not legitimate under the Constitution. Equal rights for blacks had not survived the democratic process in much of the country. But the Constitution protected the right to be treated equally even if it was not popular. That is what the Constitution and the Bill of Rights stand for, in fact that is what our country stands for.
The ballot initiative process when it deals with civil rights is an inappropriate use of democratic government. (There are many other reasons I think the ballot initiative process not a good idea but I won't go into those today.) Can anyone imagine holding a ballot initiative to determine if Nazis can have free speech? Make no misstate, I am not a fan of Nazi's but I am a big fan of the Bill of Rights.
The Courts in California have held (rightly I think) that denying marriage to gay men and lesbians is a violation of the equal protection clause of the US and California constitutions. Just like Brown v. The Broad of Ed. it was not popular. The referendum process should not be used to overturn something that is protected by the Constitution.