It sounds really out there, but how else is progress going to come about unless someone takes a chance? Didn't Captain Kirk say "risk is our business?" And while we're not in the dangerous position of helming a starship into space, we are willing to risk the snickers from other humans when we say we want to see more Star Trek coming to life. That is exactly what a group of engineers did in 2013, according to a report by Giant Freakin' Robot. They started a petition to ask that a feasibility study be conducted to build the Enterprise.
A website, which is now defunct, called BuildTheEnterprise.org, detailed the specifications of the ship. Created by an engineer who believed the Enterprise could be built within twenty years, the website included conceptual designs and even a funding schedule. A video was even uploaded to Youtube to describe how to build a gravity wheel.
Unfortunately, the petition to the White House only reached 25,000 signatures, and 32,000 signatures are required for the petition to be officially considered. A peitition to build the Death Star from Star Wars did reach the proper amount of signatures, but it wasn't really considered by the White House.
Will there ever come a time when we'll be able to build starships, and space travel is an every day occurrence? It's entirely possible, considering how far we've come with Star Trek technology. You can visit Ex Astris Scientia to take a look at what has actually been created and is being utilized today. Before a starship can be built, we have a lot more to learn about space, and there's plenty of time. It wasn't until 2246 that the Enterprise officially launched on its first five-year mission. So we still have over two hundred years to build something equivalent.