Energy independence can be understood to mean different things: Being unaffected by price changes and importing no energy from outside the country; or just importing no energy whatsoever from outside the country; or not relying to a significant degree on foreign energy sources.
The U.S. economy is not autarchic and so the country will be influenced by the price of energy elsewhere, such as by a closure of the Straits of Hormuz. It makes sense to trade in energy as in other commodities, so no commerce in energy is a foolish idea. But, thanks to new technologies, the United States can became self-sufficient in the third, more restricted meaning of the phrase.
I predict this because every effort at locating a "peak oil" moment has failed; it's time to give up this notion (along with Malthusian economics) and expect that human ingenuity will keep discovering new sources of energy. Indeed, the advanced countries are probably just at the beginning of the smart exploration of underground resources. For example, recent Japanese exploration for methane hydrate in its own surrounding waters has turned up vast supplies that could take care of Japan's energy needs for a century. Limiting our imagination to known resources is a nearly-sure way to get things wrong.
So, I argue that Americans can and will be energy independent.