Well, there are at least two, and if it holds up, three amendments that will come into play here:
14th Amendment: The "equal protection" clause. It claims that everyone is entitled to equal protection under the law. In my mind, that extends to any individual that wants to claim the same right as another individual. For example, if two consenting men/women want to be married, they have "equal protection" under the law, and constitutionally should be able to.
9th Amendment: Non enumerated rights (this one is not nearly as powerful as the 14th). It holds that the Constitution doesn't have to specifically grant us all of our civil liberties. It has been used successfully against sodomy laws that governed acts between a man and his wife, and things of that nature.
If it passes: 4th Amendment -- Full Faith & Credit -- That means that any marriage performed in states where gay marriage is legal will be honored fully in any state that forbids it.
Rev: It's not about mob rule here, it's about what the constitution says. In this case, there must either be an amendment forbidding gay marriage, or it will be legal under the current constitution if any judge follows what it says to the letter.
Please note, I'm not making any values statements here, saying it's right or wrong, those are just the facts as they are (of course, any interpretation of the constitution is debatable, but that's how this court and many others see it).
Also, we don't live in a Democratic state. It's a Democratic Republic that is set up by a Constitution -- I know.. common mistake